Injectivity Radius of Compact Riemannian Manifold is Positive

Theorem

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

Let $\map {\operatorname{inj} } M$ be the injectivity radius of $M$.

Then $\map {\operatorname{inj} } M > 0$.

Proof

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Sources

• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 6$: Geodesics and Distance. Uniformly Normal Neighborhoods