Grundlagen der Gewebelehre

* * * z - Ebene → → → → w = tan(z) → → → → → → w - Ebene * * *
[size=50][left]Dies ist ein [color=#0000ff][b]Bild[/b][/color] des Applets auf der [url=https://www.geogebra.org/m/kCxvMbHb#material/jnCvsQKx]vorigen Seite[/url][/left][br][right]Diese Seite ist Teil des GeoGebra-Books [url=https://www.geogebra.org/m/kCxvMbHb]Moebiusebene[/url]. [color=#ff7700][b](Juli 2019)[/b][/color][/right][br][size=100]Was ist ein [color=#ff0000][i][b]Sechs-Eck-Netz[/b][/i][/color] oder (synonym) ein [color=#ff0000][i][b]Sechs-Eck-Gewebe[/b][/i][/color][/size] ([size=85]manchmal auch [color=#ff0000][i][b]Drei-Ecks-Netz[/b][/i][/color])[/size]?[br][br][size=85]Die folgende "Definition" ist nicht unter dem Aspekt größtmöglicher mathematischer Präzision, sondern mit dem Ziel formuliert, [br]so weit möglich ein anschauliches Bild vom Sachverhalt zu entwerfen.[br][br]Drei Kurvenscharen in einem offenen Gebiet der Ebene sollen die folgenden Eigenschaften aufweisen:[br][/size][list][*][size=85]Durch jeden Punkt der Ebene geht aus jeder der drei Scharen genau eine Kurve.[/size][/*][*][size=85]Jede Kurve einer Schar schneidet jede einzelne Kurve einer der anderen Scharen in genau einem Punkt. (*)[/size][br][/*][/list][size=85]Dann bilden die drei Kurvenscharen ein [color=#ff0000][i][b]Sechs-Eck-Gewebe[/b][/i][/color], wenn folgende Schließungsbedingung erfüllt ist:[br][table][tr][td][size=85]Es sei [math]p_0[/math] irgendein Punkt des Gebiets und es seien [math]k_{10}[/math], [math]k_{20}[/math] und [math]k_{30}[/math] die drei Kurven durch [math]p_0[/math]. [br][math]p_1[/math] sei irgendein ein 2.ter Punkt auf einer der drei Kurven, zB. auf [math]k_{10}[/math].[br]Die Kurven [math]k_{31}[/math] und [math]k_{21}[/math] durch [math]p_1[/math] schneiden [math]k_{20}[/math], bzw. [math]k_{30}[/math] in den Punkten [math]p_2[/math] bzw. [math]p_3[/math]. [br]Die Kurve [math]k_{11}[/math] durch [math]p_2[/math] schneidet [math]k_{30}[/math] in [math]p_4[/math]. [br]Die Kurve [math]k_{12}[/math] durch [math]p_3[/math] schneidet [math]k_{20}[/math] in [math]p_5[/math]. [br]Die Kurven [math]k_{22}[/math] durch [math]p_4[/math] und [math]k_{32}[/math] durch [math]p_5[/math] schneiden sich auf [math]k_{10}[/math].[br]Das [color=#ff0000][i][b]Sechs-Eck[/b][/i][/color] schließt sich in diesem Schnitt-Punkt [math]p_6[/math] 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[/img][/td][/tr][/table][br]Die Frage, ob 3 Kurvenscharen in der Ebene ein [color=#ff0000][i][b]Sechs-Eck-Gewebe[/b][/i][/color] bilden, ist einfach zu beantworten: [i][b]Meistens nicht[/b][/i]![br][color=#0000ff][i][b]Welche Methoden[/b][/i][/color] gibt es, Sechs-Eck-Gewebe zu erkennen?[br]Die Methoden zum Nachweis für das Vorliegen eines Sechs-Eck-Gewebe sind erstaunlich vielfältig. [br]Wir wollen sie hier aufzählen, teilweise ohne exakten Beweis.[br][br][size=50](*) Diese Bedingung ist für Netze aus Kreisen zu streng: Zwei Kreise können sich in 2 Punkten schneiden, sie können sich berühren (1 Schnittpunkt) [br]oder sie können sich überhaupt nicht schneiden. Diese 3 Fälle liegen oft nahe beieinander! Die auf den folgenden Seiten angezeigten Beispiele [br]von Sechs-Eck-Netzen aus Kreisen lassen die genannten 3 Fälle an den Rändern des Gültigkeitsbereiches gut erkennen.[br][/size][br][color=#0000ff][i][b]Drei Parallelenscharen[/b][/i][/color] in drei verschiedenen Richtungen bilden stets ein [color=#ff0000][i][b]Sechseck-Gewebe[/b][/i][/color].[br]Dies sieht man leicht mit Hilfe der Vektorrechnung ein: Es sei [math]\vec{\mathbf{a}}=\overrightarrow{P_0P_1}[/math] eine der drei Parallelen-Richtungen. [br]Die beiden anderen Richtungsvektoren [math]\vec{\mathbf{b}}[/math], [math]\vec{\mathbf{c}}[/math] kann man so normieren, dass [math]\vec{\mathbf{c}}=\vec{\mathbf{a}}-\vec{\mathbf{b}}[/math] gilt. [br]Dann wird das Sechs-Eck-Gewebe punktweise durch [math] P_0+k_1\cdot\vec{\mathbf{a}} +k_2\cdot\vec{\mathbf{b}}[/math] mit [math]k_1,k_2\in\mathbb{Z}[/math] erzeugt.[br]Die Parallelenscharen kann man beschreiben durch Funktionen [math]\varphi_1\left(x,y\right)=\alpha\cdot x+\beta\cdot x=const[/math], [br][math]\varphi_2\left(x,y\right)=\gamma\cdot x+\delta\cdot y=const[/math] und [math]\varphi_3\left(x,y\right)=\sigma\cdot x+\tau\cdot y=const[/math] mit reellen Koeffizienten, die man so wählen kann, [br]dass [math]\varphi_1+\varphi_2+\varphi_3\equiv0[/math] gilt.[br]Wir nennen diese Netze aus 3 Parallelenscharen im Folgenden öfters "Standard-Netze".[br][br][color=#980000][i][b]Methode I: [/b][/i][/color] Bildet man die Parallelen eines Standard-Netzes in einem Gebiet der Ebene ab mit einem [color=#980000][i][b]Diffeomorphismus[/b][/i][/color], [br]so bilden die Bildkurven ein [color=#ff0000][i][b]Sechs-Eck-Netz[/b][/i][/color]. [br]Besonders schön werden die Bilder mit [i][b][color=#0000ff]konformen[/color] [/b][/i]Abbildungen in der [b]GAUSS[/b]schen Zahlenebene. [br][color=#0000ff][i][b]Konforme[/b][/i][/color] Abbildungen sind komplex-differenzierbare oder meromorphe Funktionen, ohne Nullstellen der Ableitung [br]in dem fraglichen Bereich; sie sind [color=#0000ff][i][b]winkeltreu[/b][/i][/color], d.h. die Winkel in einem Netz aus 3 Parallelen-Scharen bleiben [br]unter der Abbildung erhalten.[br]Die Abbildung eines [color=#ff0000][i][b]Standard-Netzes[/b][/i][/color] mit solchen komplex-differenzierbaren Funktionen ist unserer Meinung [br]nach ein besonders nützliches und schönes Hilfsmittel, um die geometrischen Eigenschaften dieser Funktionen zu erkunden.[br]Oben und auf der Seite zuvor ist das Bild eines [color=#ff0000][i][b]Standard-Netzes[/b][/i][/color] unter der komplexen [math]\mathbf{tan}[/math]-Funktion dargestellt.[br][br]Es gilt auch die Umkehrung der obigen Aussage: [br]Jedes [color=#ff0000][i][b]Sechs-Eck-Gewebe[/b][/i][/color] ist das [color=#980000][i][b]diffeomorphe Bild[/b][/i][/color] eines [color=#ff0000][i][b]Standard-Sechseck-Gewebes [/b][/i][/color]aus drei [color=#0000ff][i][b]Parallelen-Scharen[/b][/i][/color], [br]zumindest in einem geeigneten offenen Beeich der Ebene und sofern naheliegende Differenzierbarkeits- und [br]Regularitätsbedingungen erfüllt sind.[br][/size][/size]
Sechseck-6-Netz
[size=85][color=#980000][i][b]Methode II:[/b][/i][/color] Sind drei Kurvenscharen implizit gegeben als Niveaulinien dreier reellwertigen Funktionen:[br][list][*][math]\varphi_1\left(x,y\right)=const[/math], [math]\varphi_2\left(x,y\right)=const[/math] und [math]\varphi_3\left(x,y\right)=const[/math] mit [math]\varphi_1+\varphi_2+\varphi_3\equiv0[/math][/*][/list]so bilden die 3 Kurvenscharen ein [color=#ff0000][i][b]Sechs-Eck-Gewebe[/b][/i][/color], sofern die nötigen Differenzierbarkeits- und [br]Regularitätsbedingungen erfüllt sind.[br]Für [color=#0000ff][i][b]drei Parallelenscharen[/b][/i][/color] haben wir solche Funktionen angegeben (siehe vor [color=#980000][i][b]Methode I[/b][/i][/color]).[br]Im [i][b]Applet[/b][/i] oben ist ein ganz besonderes [color=#ff0000][i][b]Sechs-Eck-Netz[/b][/i][/color] zu sehen: [color=#0000ff][i][b]Drei Geradenbüschel[/b][/i][/color] erzeugen stets [br]ein [color=#ff0000][i][b]Sechs-Eck-Netz[/b][/i][/color].[br]Dies ist für sich schon bemerkenswert: die [color=#38761D][i][b]euklidischen Streckungen[/b][/i][/color] der Ebene mit verschiedenen Zentren [br]sind [i][b]nicht[/b][/i] vertauschbar, während Verschiebungen es sind (Vektoraddition!). Die [color=#ff0000][i][b]Sechs-Eck-Bedingung[/b][/i][/color] muss also [br]für 3 Geradenbüschel mit verschiedenen Zentren anders als für 3 [color=#0000ff][i][b]Parallelenscharen [/b][/i][/color]begründet werden.[br]Oben wird das [color=#ff0000][i][b]Sechs-Eck-Netz[/b][/i][/color] obendrein ergänzt durch 3 Kegelschnittbüschel: die Kegelschnitte durch 2 der Zentren [br]mit den Verbindungsgeraden zum 3. Zentrum als Tangenten.[br]Je drei diese 6 Kurvenscharen bilden ein [color=#ff0000][i][b]Sechs-Eck-Gewebe[/b][/i][/color], die anderen 3 Kurvenscharen liefern die Diagonalen [br]des Netzes.[br]Ein Gewebe aus [math]n[/math] Kurvenscharen, von denen je 3 ein [color=#ff0000][i][b]Sechs-Eck-Gewebe[/b][/i][/color] bilden, wird [color=#ff7700][i][b]Sechseck-n-Geweb[/b][/i][i][b]e[/b][/i][/color] genannt, [br]siehe dazu das Buch [b][BLA_BO][/b] "[i]Geometrie der Gewebe[/i]" von [b]W. BLASCHKE[/b] und [b]G. BOL[/b] (1938) ([url=https://www.geogebra.org/m/kCxvMbHb#material/kBuDGYqv]Literaturverzeichnis[/url]).[br]Oben liegt also ein [color=#ff7700][i][b]Sechseck-6-Gewebe[/b][/i][/color] vor.[br][color=#980000][i][b]Begründung (Kurzfassung):[/b][/i][/color][br]In geeigneten homogenen Koordinaten [math](u,v,w)[/math] sind diese sechs Kurvenscharen Niveaulinien der Funktionen:[br][list][*][math]\varphi_1=ln\frac{u}{v}[/math], [math]\varphi_2=ln\frac{v}{w}[/math], [math]\varphi_3=ln\frac{w}{u}[/math]; [/*][*]und [math]\varphi_4=\varphi_1-\varphi_2=ln\frac{uw}{v^2}[/math], [math]\varphi_5=\varphi_2-\varphi_3=ln\frac{vu}{w^2}[/math], [math]\varphi_6=\varphi_3-\varphi_1=ln\frac{wv}{u^2}[/math][/*][/list][size=50]Das Verständnis von "homogenen Koordinaten" setzt ein wenig Vertrautheit mit projektiven Denkweisen voraus. Wir wollen das hier nicht vertiefen![/size][/size]
[size=85][i][b][color=#980000]Methode III[/color]:[/b][/i] Gibt es zu einem Gewebe aus drei Kurvenscharen [math]\mathfrak{S}_{1,}\mathfrak{S}_2,\mathfrak{S}_3[/math] eine Ein-Parameter-Gruppe [math]t\mapsto A\left(t\right)[/math] von Abbildungen, für welche die Kurven von [math]\mathfrak{S}_1[/math] Bahnkurven sind und die Kurvensysteme [math]\mathfrak{S}_{2},\mathfrak{S}_3[/math] als Ganzes festbleiben, so ist das Gewebe ein [color=#ff0000][i][b]Sechs-Eck-Gewebe[/b][/i][/color]. Die oben genannten Voraussetzungen an die 3 Kurvenscharen mögen vorliegen.[br][table][tr][td]Zur [color=#980000][u][i]Begründung[/i][/u][/color] zeigen wir, dass sich jede Sechs-Eck-Figur schließt - zumindest im Kleinen.[br]Es seien [math]\gamma_1,\gamma_2,\gamma_3[/math] die 3 Kurven aus den 3 Scharen durch einen vorgegebenen Punkt [math]p_0[/math], und es sei [math]p_1[/math] ein zweiter Punkt, etwa auf [math]\gamma_2[/math]. [math]\tilde{\gamma_2},\tilde{\gamma_3}[/math] seien die Bildkurven unter derjenigen Abbildung [math]\mathbf{A}[/math] aus der Gruppe, für welche [math]\tilde{\gamma_3}[/math] durch [math]p_1[/math] geht. Die Kurven [math]\gamma_2,\gamma_3,\tilde{\gamma_2},\tilde{\gamma_3}[/math] bilden eine "Raute" mit den Schnittpunkten [math]p_0,p_1,p_2,p_3[/math]. Die Abbildung [math]\mathbf{A^{-1}}[/math] ergänzt das [color=#ff0000][i][b]Sechs-Eck[/b][/i][/color], die fehlenden 2 Kurven [math]\tilde{\gamma_3} , \tilde{\gamma_4} [/math] sind die Bahnkurven durch [math]p_1[/math] und [math]p_3[/math].[/td][td][img]data:image/png;base64,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[/img][/td][/tr][/table][/size]
[size=85][br][color=#980000][i][b]Methode IV:[/b][/i][/color] Wieder liege ein Gewebe aus 3 Kurvenscharen [math]\mathfrak{S}_{1,}\mathfrak{S}_2,\mathfrak{S}_3[/math] mit den genannten Voraussetzungen vor. [br]Zu jeder Kurve [math]\gamma\in \mathfrak{S}_1[/math] möge es eine 'Spiegelung' geben, d.i. eine [i][b]involutorische[/b][/i] Abbildung, welche [math]\gamma[/math] punktweise festläßt.[br]Wenn diese 'Spiegelungen' [math]\mathfrak{S}_1[/math] als Ganzes festlassen, und sie die beiden anderen Kurvenscharen [math]\mathfrak{S}_2, \mathfrak{S}_3[/math] vertauschen, [br]dann bilden die 3 Scharen ein [color=#ff0000][i][b]Sechs-Eck-Gewebe[/b][/i][/color].[br][table][tr][td][img]data:image/png;base64,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[/img][/td][td][color=#980000][u][i]Begründung[/i][/u][/color]: Es seien wie oben [math]\gamma_1,\gamma_2,\gamma_3[/math] die Kurven durch einen Punkt [math]p_0[/math] [br]und [math]p_1[/math] ein weiterer Punkt, beispielsweise auf [math]\gamma_2[/math]. [br]Die Kurve [math]\tilde{\gamma_3}[/math] durch [math]p_1[/math] schneide [math]\gamma_2[/math] in [math]p_2[/math].[br]Die Kurve [math]\tilde{\gamma_1}[/math] durch [math]p_1[/math] schneide [math]\gamma_3[/math] in [math]p_3[/math].[br]Die Kurve [math]\tilde{\gamma_2}[/math] durch [math]p_3[/math] schneide [math]\gamma_1[/math] in [math]p_4[/math].[br]Die Spiegelung an [math]\gamma_1[/math] ergänzt die Figur zur Sechseckfigur.[br] [/td][/tr][/table]In den Applets oben und unten ist [color=#073763][i][b]links[/b][/i][/color] ein Beispiel für die [color=#980000][i][b]Methode III[/b][/i][/color], und [color=#a61c00][i][b]rechts[/b][/i][/color] eines für die [color=#980000][i][b]Methode IV[/b][/i][/color] dargestellt.[br]Die Bahnkurven sind [color=#073763][i][b]links[/b][/i][/color] die Kreise des hyperbolischen Kreisbüschel um die beiden Grundpunkte, unten sind [br]das 0 und [math]\infty[/math], die Bewegungen sind die [color=#0000ff][i][b]Drehungen[/b][/i][/color] um die Grundpunkte.[br]Die Spiegelungen [i][b][color=#a61c00]rechts[/color][/b][/i] sind die [i][b][color=#a61c00]Spiegelungen[/color][/b][/i] an den [/size][size=85][size=85]hyperbolischen[/size] Kreisen. [br]Die Schar der Berührkreise bleibt bei den [color=#0000ff][i][b]Drehungen[/b][/i][/color] wie bei den [color=#a61c00][i][b]Spiegelungen[/b][/i][/color] erhalten![/size]
[size=85][color=#980000][i][b]Methode V:[/b][/i][/color] Konstruktion mit drei [color=#9900ff][i][b]Vektorfeldern[/b][/i][/color][br]Eine Kurvenschar aus differenzierbaren Kurven in einem offenen Gebiet derart, dass durch jeden Punkt genau eine Kurven [br]mit nicht-verschwindender Ableitung geht, legt ein[color=#9900ff][i][b] Vektorfeld[/b][/i][/color] in diesem Gebiet fest.[br]Zu drei Kurvenscharen gehören, genügende Differenzierbarkeit vorausgesetzt, 3 [color=#9900ff][i][b]Vektorfelder[color=#000000] [math]X_1,X_2,X_3[/math]. [br][/color][/b][/i][color=#000000]Wenn man weiter voraussetzt, dass diese Kurven sich in dem offenen Gebiet nirgends berühren, so zeigen die [br]Tangentialvektoren in jedem Punkt in 3 verschiedene Richtungen. In der Ebene sind 3 Vektoren linear abhängig, [br]es muss daher möglich sein, durch geeignete differenzierbare Umnormierung [math]\widetilde{X_i}=\sigma\cdot X_i[/math] mit differenzierbaren [br]Funktionen [math]\sigma_i,i=1,2,3[/math] zu erreichen, dass gilt:[/color][/color][br][list][*] [math]\widetilde{X_1}+\widetilde{X_2}+\widetilde{X_3}\equiv0[/math] [/*][/list]Beschreibt man das [color=#ff0000][i][b]Standard-Sechs-Eck-Gewebe[/b][/i][/color] der drei Parallelenscharen [br][list][*][math]x=const[/math], [math]y=const[/math], [math]y-x=const[/math] durch die [color=#38761D][i][b]Vektorfelder[/b][/i][/color] [math]X_1=\partial_y[/math], [math]X_2=\partial_y[/math] und [math]X_3=-\left(\partial_x+\partial_y\right)[/math][br][/*][/list]so ist die Bedingung [math]X_1+X_2+X_3\equiv0[/math] erfüllt. Überdies gilt in diesem Falle: [math]\left[X_i,X_j\right]\equiv0[/math].[br]Das [b]LIE-Produkt[/b] zweier [color=#38761D][i][b]Vektorfelder[/b][/i][/color] [math]X,Y[/math] ist dabei erklärt durch: [math]\left[X,Y\right]\varphi:=X\left(Y\varphi\right)-Y\left(X\varphi\right)[/math]. [br]Es gelten die Regeln:[list][*][math]X\varphi\cdot\psi=\psi\left(X\varphi\right)+\varphi\left(X\psi\right)[/math][br][/*][*][math]\left[\psi X,\varphi Y\right]=\psi\cdot\varphi\left[X,Y\right]+\psi\left(X\varphi\right)Y-\varphi\left(Y\psi\right)X[/math][br][/*][/list][u][color=#38761D][i][b]Kriterium:[/b][/i][/color][/u] Ein Gewebe [math]\mathfrak{W}^3[/math] werde beschrieben durch die drei Vektorfelder [math]X_1,X_2,X_3[/math] mit [math]X_1+X_2+X_3\equiv0[/math].[br]Das Gewebe ist genau dann ein SechsEck-Gewebe, wenn eine gemeinsame Umnormierung [math]\widetilde{X_i}=\sigma\cdot X_i[/math], [math]\sigma\ne0[/math] existiert, [br]so dass das [b]LIE-Produkt[/b] verschwindet:[list][*][math]\left[\widetilde{X_i},\widetilde{X_j}\right]\equiv0,i,j=1,2,3[/math][br][/*][/list]Wir wollen im Folgenden die [color=#ff0000][i][b]Sechs-Eck-Gewebe[/b][/i][/color] aus [color=#0000ff][i][b]Kreisbüscheln[/b][/i][/color] bestimmen. [br]Dazu formulieren wir das [color=#38761D][u][i][b]Kriterium[/b][/i][/u][/color] in einer uns nützlichen Form:[br][list][*]Für die Vektorfelder [math]X_1,X_2,X_3[/math] gelte in einem Gebiet [br][list][*][math]\lambda_1X_1+\lambda_2X_2+\lambda_3X_3\equiv0[/math] mit nirgends verschwindenden reellwertigen Funktionen [math]\lambda_i[/math], [/*][br][*]und es sei [math]\left[X_1,X_2\right]=\tau_1X_1-\tau_2X_2[/math]. [br][/*][/list]Die Integralkurven bilden genau dann ein [size=85][color=#ff0000][i][b]Sechs-Eck-Gewebe[/b][/i][/color][/size], wenn gilt: [br][list][*][math]X_1\tau_1-X_2\tau_2+\tau_1\cdot\frac{X_1\lambda_2}{\lambda_2}-\tau_2\cdot\frac{X_2\lambda_1}{\lambda_1}+X_2\frac{X_1\lambda_2}{\lambda_2}-X_1\frac{X_2\lambda_1}{\lambda_1}\equiv0[/math][br][/*][/list][/*][/list][/size]
[br][table] [tr][br] [td][size=85]Wir hatten die Infinitesimalen von Keisbüscheln als [color=#38761D][i][b]Vektorfelder[/b][/i][/color] gedeutet. Zwei Infinitesimale sind nur dann vertauschbar, d.h. ihr [b]LIE-Produkt[/b] ist 0, wenn sie zu demselben hyperbolischen, bzw. parabolischen Kreisbüschel gehören.[br]Es sei also z.B. [math]\mathbf\vec{g}\in \mathcal{G}[/math] ein hyperbolisches Kreisbüschel. Die Vektorfelder [math]X_1=a\cdot \mathbf\vec{g},X_2=b\cdot \mathbf\vec{g},X_3=-(a+b)\cdot \mathbf\vec{g}[/math] erfüllen das obige Kriterium, wenn [math]a,b\in \mathbb{C}[/math] nicht reell abhängig sind. [br][br]Es handelt sich um ein Sechs-Eck-Gewebe aus Kurven, die die Kreise des [color=#0000ff][i][b]hyperbolischen Kreisbüschels[/b][/i][/color] [math]\mathbf\vec{g}[/math] unter 3 verschiedenen Winkeln schneiden: [br]das [i][b]Deckblatt [/b][/i]dieses [color=#980000][i][b]ge[/b][/i][/color][icon]https://www.geogebra.org/images/ggb/toolbar/mode_conic5.png[/icon][color=#980000][i][b]gebra-books[/b][/i][/color] zeigt ein solches [color=#ff0000][i][b]Sechs-Eck-Gewebe[/b][/i][/color].[/size][/td][td][img]data:image/png;base64,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[/img][/td][br][/tr][br][/table]
Diese Aktivität als PDF-Datei: Grundlagen der Gewebelehre - GeoGebra

Information: Grundlagen der Gewebelehre