From 10bc309a7edaf77c1ea290e0034b533f97d26de5 Mon Sep 17 00:00:00 2001 From: Martin Thoma Date: Tue, 26 Nov 2013 23:13:24 +0100 Subject: [PATCH] Doppelte Definition entfernt. 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z1BY^80U);KRf5eMY&8k<&@Bg9MSTlGd&B90@&_>K941y$7_mW`5LR3t$RU7hjvu`Ul(lP6~v)s2H*1JL%wI< zR_U}~TU2?t41>7FKY2aWx<(-g*CIZ2phukuJmGNT5yDkZ8klGNcx!J^tchQ^u|jZz z`sZQnQNAd3^+>P31=$}`=q2zT5DH!>Zk9yN;8>JTIyUf*5b|sUHY`HnZsJM!@en5$ zjBG@)pr6yy|8%#KXYe7MSpLClsBob7ih(s^;+GX5gjd96OJv&riysG!rYD4l$|u0Z NgF;U)r!J53e*ip_+wA}V diff --git a/documents/GeoTopo/Kapitel2.tex b/documents/GeoTopo/Kapitel2.tex index d83f053..d9ca228 100644 --- a/documents/GeoTopo/Kapitel2.tex +++ b/documents/GeoTopo/Kapitel2.tex @@ -360,10 +360,11 @@ $\partial X$ ist eine Mannigfaltigkeit der Dimension $n-1$. \end{bemerkung} \begin{definition} - Eine Teilmenge $S \subseteq \mdr^3$ heißt \textbf{reguläre Fläche}\xindex{Fläche!reguläre}, - wenn es für jedes $s \in S$ eine Umgebung $V$ von $\sin{\mdr^3}$ - eine offene Teilmenge $F: U \rightarrow V \cap S$ gibt, sodass - die Jacobi-Matrix $J_F(u)$ für alle $u \in U$ Rang 2 hat. + $S \subseteq \mdr^3$ heißt \textbf{reguläre Fläche}\xindex{Fläche!reguläre} $:\gdw$ + zu $s \in S$ ex. eine Umgebung $V \subseteq \mdr^3$ und offene + Teilmengen $U \subseteq \mdr^2$ und differenzierbare Abbildung + $F: U \rightarrow V \cap S$ mit $\text{Rg}(J_f(u)) = 2$ + für alle $u \in U$. $F$ heißt (lokale) reguläre Parametrisierung von $S$. @@ -436,14 +437,6 @@ $\partial X$ ist eine Mannigfaltigkeit der Dimension $n-1$. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Mitschrieb vom 21.11.2013 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{definition} - $S \subseteq \mdr^3$ heißt \textbf{reguläre Fläche}\xindex{Fläche!reguläre} $:\gdw$ - zu $s \in S$ ex. eine Umgebung $V \subseteq \mdr^3$ und offene - Teilmengen $U \subseteq \mdr^2$ und differenzierbare Abbildung - $F: U \rightarrow V \cap S$ mit $\text{Rg}(J_f(u)) = 2$ - für alle $u \in U$. -\end{definition} - \begin{korollar} Jede reguläre Fläche $S \subseteq \mdr^3$ ist eine 2-dimensionale, differenzierbare Mannigfaltigkeit.