From 3781e7a12fe6a56ca60138b5480f92ac38dfd46d Mon Sep 17 00:00:00 2001
From: Juan Marín Noguera <juan.marinn@um.es>
Date: Fri, 15 Jan 2021 11:55:46 +0100
Subject: GCS formato

---
 gcs/n3.lyx | 15 +++++++++------
 1 file changed, 9 insertions(+), 6 deletions(-)

diff --git a/gcs/n3.lyx b/gcs/n3.lyx
index a3246ce..02ffa54 100644
--- a/gcs/n3.lyx
+++ b/gcs/n3.lyx
@@ -1794,10 +1794,15 @@ curvatura geodésica
 
 .
  En efecto, 
-\begin_inset Formula $\langle\frac{D\alpha'}{ds}(s),\alpha'(s)\rangle=\langle\alpha''(s)-\langle\alpha''(s),N(\alpha(s))\rangle N(\alpha(s)),\alpha'(s)\rangle=\langle\alpha''(s),\alpha'(s)\rangle-\langle\alpha''(s),N(\alpha(s))\rangle\langle N(\alpha(s)),\alpha'(s)\rangle=0$
+\begin_inset Formula 
+\begin{multline*}
+\langle\frac{D\alpha'}{ds}(s),\alpha'(s)\rangle=\langle\alpha''(s)-\langle\alpha''(s),N(\alpha(s))\rangle N(\alpha(s)),\alpha'(s)\rangle=\\
+=\langle\alpha''(s),\alpha'(s)\rangle-\langle\alpha''(s),N(\alpha(s))\rangle\langle N(\alpha(s)),\alpha'(s)\rangle=0,
+\end{multline*}
+
 \end_inset
 
-, y 
+y 
 \begin_inset Formula $\kappa_{g}(s)=\langle\frac{D\alpha'}{ds}(s),J\alpha'(s)\rangle=\langle\alpha''(s),J\alpha'(s)\rangle$
 \end_inset
 
@@ -3186,14 +3191,12 @@ F & G
 f & g
 \end{pmatrix}\begin{pmatrix}G & -F\\
 -F & E
-\end{pmatrix}=\frac{1}{EG-F^{2}}\begin{pmatrix}fF-eG & eF-fE\\
-gF-fG & fF-gE
-\end{pmatrix}.
+\end{pmatrix},
 \]
 
 \end_inset
 
-
+lo que nos da las fórmulas de Weingarten.
 \end_layout
 
 \begin_layout Standard
-- 
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