Talk:Fermi coordinates
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Curvature depends on the derivative of the Christoffel's. The statement
" For example, if all Christoffel symbols vanish near p, then the manifold is flat near p."
is wrong. — Preceding unsigned comment added by 212.239.166.151 (talk) 09:36, 23 April 2009 (UTC)
- I don't think so. That the christoffel symbols vanish near p means that p has a neighborhood where the Christoffel symbols vanish. Then also the derivatives vanish, and hence curvature vanishes in this neighborhood. Haseldon (talk)
Riemannian Geometry is the wrong context for Fermi coordinates.
[edit]The term, Riemannian, is usually understood to exclude (although it arguably shouldn't) metric forms that are hyperbolic, in the sense that their eigenvalues have differing signs. The primary context for Fermi coordinates is a 4-dimensional Lorentzian manifold, a Lorentzian manifold more generally, perhaps more generally still a pseudo-Riemannian or semi-Riemannian manifold. But it's clearly erroneous to exclude hyperbolic forms. Taabagg (talk) 07:19, 12 June 2021 (UTC)
Fermi coordinates for Semi-Riemannian Submanifolds
[edit]I already added a citation [1] for Fermi coordinates for Riemannian Submanifolds, how about the Semi-Riemannian Submanifold case? Pmokeefe (talk) 12:43, 26 October 2024 (UTC)
- ^ Lee, John M. (2019-01-02). Introduction to Riemannian Manifolds. Cham, Switzerland: Springer. p. 136. ISBN 978-3-319-91755-9.