Gauss Lemma for Riemannian Manifolds

From ProofWiki
Jump to navigation Jump to search

Theorem

Let $\struct {M, g}$ be a Riemannian manifold.

Let $U = \map {\exp_p} {\map {B_\epsilon} 0 }$ be a geodesic ball centered at $p \in M$.

Let $\partial_r$ be the radial vector field on $U \setminus \set p$, where $\setminus$ denotes the set difference.


Then $\partial_r$ is a unit vector field orthogonal to the geodesic spheres in $U \setminus \set p$.


Proof




Source of Name

This entry was named for Carl Friedrich Gauss.


Sources