diff options
Diffstat (limited to 'ggs/n3.lyx')
| -rw-r--r-- | ggs/n3.lyx | 21 |
1 files changed, 15 insertions, 6 deletions
@@ -1194,11 +1194,15 @@ Sean \end_inset Entonces -\begin_inset Formula $\Vert\alpha'(t)\Vert^{2}=r'(t)^{2}\Vert d(\exp_{p_{0}})_{\tilde{\alpha}(t)}(V(t))\Vert^{2}+2r(t)r'(t)\langle d(\exp_{p_{0}})_{\tilde{\alpha}(t)}(V(t)),d(\exp_{p_{0}})_{\tilde{\alpha}(t)}(V'(t))\rangle+r(t)^{2}\Vert d(\exp_{p_{0}})_{\tilde{\alpha}(t)}(V'(t))\Vert^{2}$ +\begin_inset Formula +\begin{align*} +\Vert\alpha'(t)\Vert^{2}= & r'(t)^{2}\Vert d(\exp_{p_{0}})_{\tilde{\alpha}(t)}(V(t))\Vert^{2}\\ + & +2r(t)r'(t)\langle d(\exp_{p_{0}})_{\tilde{\alpha}(t)}(V(t)),d(\exp_{p_{0}})_{\tilde{\alpha}(t)}(V'(t))\rangle+r(t)^{2}\Vert d(\exp_{p_{0}})_{\tilde{\alpha}(t)}(V'(t))\Vert^{2}. +\end{align*} + \end_inset -. - Como +Como \begin_inset Formula $V(t)$ \end_inset @@ -1211,10 +1215,14 @@ Entonces \end_inset , luego -\begin_inset Formula $\langle r(t)V(t),V'(t)\rangle=r(t)\langle V(t),V'(t)\rangle=0$ +\begin_inset Formula +\[ +\langle r(t)V(t),V'(t)\rangle=r(t)\langle V(t),V'(t)\rangle=0 +\] + \end_inset - y +y \begin_inset Formula \begin{multline*} \langle d(\exp_{p_{0}})_{\tilde{\alpha}(t)}(V(t)),d(\exp_{p_{0}})_{\tilde{\alpha}(t)}(V'(t))\rangle=\\ @@ -1881,7 +1889,8 @@ queda pero \begin_inset Formula \begin{multline*} -\lim_{r\to0}\frac{\partial}{\partial r}\left(\sqrt{\overline{E}\overline{G}-\overline{F}^{2}}(r_{\theta})\right)=\lim_{r\to0}\frac{\frac{\partial}{\partial r}(\overline{E}(r_{\theta}))\overline{G}(r_{\theta})+\overline{E}(r_{\theta})\frac{\partial}{\partial r}(\overline{G}(r_{\theta}))-2\overline{F}(r_{\theta})\frac{\partial}{\partial r}(\overline{F}(r_{\theta}))}{2\sqrt{\overline{E}\overline{G}-\overline{F}^{2}}(r_{\theta})}\in\mathbb{R}, +\lim_{r\to0}\frac{\partial}{\partial r}\left(\sqrt{\overline{E}\overline{G}-\overline{F}^{2}}(r_{\theta})\right)=\\ +=\lim_{r\to0}\frac{\frac{\partial}{\partial r}(\overline{E}(r_{\theta}))\overline{G}(r_{\theta})+\overline{E}(r_{\theta})\frac{\partial}{\partial r}(\overline{G}(r_{\theta}))-2\overline{F}(r_{\theta})\frac{\partial}{\partial r}(\overline{F}(r_{\theta}))}{2\sqrt{\overline{E}\overline{G}-\overline{F}^{2}}(r_{\theta})}\in\mathbb{R}, \end{multline*} \end_inset |