Gauss's lemma (Riemannian geometry)

In Riemannian geometry, Gauss's lemma asserts that any sufficiently small sphere centered at a point in a Riemannian manifold is perpendicular to every geodesic through the point. More formally, let M be a Riemannian manifold, equipped with its Levi-Civita connection, and p a point of M. The exponential map is a mapping from the tangent space at p to M: e x p : T p M → M {\displaystyle \mathrm {exp} :T_{p}M\to M} which is a diffeomorphism in a neighborhood of zero.

Source: Wikipedia — Gauss's lemma (Riemannian geometry) (CC BY-SA 4.0)

Gauss's lemma (Riemannian geometry)

In Riemannian geometry, Gauss's lemma asserts that any sufficiently small sphere centered at a point in a Riemannian manifold is perpendicular to every geodesic through the point. More formally, let M be a Riemannian manifold, equipped with its Levi-Civita connection, and p a point of M. The exponential map is a mapping from the tangent space at p to M: e x p : T p M → M {\displaystyle \mathrm {exp} :T_{p}M\to M} which is a diffeomorphism in a neighborhood of zero.

Source: Wikipedia "Gauss's lemma (Riemannian geometry)" · CC BY-SA 4.0

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