Timeline for how to understand the manifold with boundary jet bundle and cotangent bundle with boundary
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 15, 2018 at 8:37 | comment | added | John Sung | I wonder whether the normal covector of $T^*M_{\partial M}$ (view it as submanifold and boundary of $T^*M$ ) has some relation with the normal covector of $\partial M$ ? | |
| Jun 14, 2018 at 17:03 | comment | added | Michael Bächtold | Yes, for your first question. I don’t quite understand your second question. What do you mean with the normal vector field? There is a canonical 1 dimensional subspace of $T^*M|_{\partial M}$ consisting of those covectors that vanish when paired with tangent vectors of the boundary. A generator of this subspace might be called a normal covector. | |
| Jun 14, 2018 at 15:34 | comment | added | John Sung | Thanks for comments. You mean view $\partial T^*(M)$ as $T^*(M)|_{\partial M}$ bundle over $\partial M$ with same $n$ dimensional fiber as $T^*(M)$ ? Is the normal vector field of $T^*(M)|_{\partial M}$ be induced from $\nu\in T_{\partial M}M$? say, for a section $s\in T^*(M)$ of cotangent bundle, is the normal vector field at point $(x,s(x))\in T^*(M)|_{\partial M} $( here, $x\in\partial M$) in $T^*(M)$ be $(\nu_x,\nu_x \lrcorner \nabla s)$? | |
| S Jun 14, 2018 at 15:09 | history | suggested | S.Surace | CC BY-SA 4.0 |
corrected spelling, grammar, and notation
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| Jun 14, 2018 at 14:54 | review | Suggested edits | |||
| S Jun 14, 2018 at 15:09 | |||||
| Jun 14, 2018 at 14:21 | comment | added | Michael Bächtold | Wouldn't $\partial T^*(M)$ be the same as $T^*(M)|_{\partial M}$ and there is a canonical projection from $T^*(M)|_{\partial M}$ to $T^*(\partial M)$ by restricting? | |
| Jun 14, 2018 at 14:03 | review | First posts | |||
| Jun 14, 2018 at 14:48 | |||||
| Jun 14, 2018 at 14:03 | history | asked | John Sung | CC BY-SA 4.0 |