Timeline for Orthonormal vector fields on a Riemannian manifold
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Dec 10, 2018 at 12:21 | comment | added | Ivan Solonenko | The first that comes to mind is the observation that $X$ is orthonormal if and only if for any $p \in M$ the differential of $X$ (considered as a map $M \to TM$) at $p$ sends $T_p M$ to the horizontal subspace $H_{(p, X_p)} \subseteq T_{(p, X_p)} (TM)$ (one just needs to unravel the definition of the Sasaki metric). But then it follows that $dX_p \colon T_p M \to H_{(p, X_p)}$ is an isometric isomorphism. | |
| Nov 11, 2018 at 21:27 | history | edited | Sylvain JULIEN | CC BY-SA 4.0 |
edited body
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| Nov 11, 2018 at 19:27 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
added 35 characters in body
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| Nov 11, 2018 at 19:22 | history | asked | Ali Taghavi | CC BY-SA 4.0 |