Injectivity radius

riemannian-geometry

Consider a surface of revolution such as $$ M = \{x \in \mathbb{R}^3 : x_1^2 + x_2^2 = \frac{1}{1+x_3^2} \} $$ with Riemannian metric inherited from the ambient space. For points with large $|x_3|$, the injectivity radius becomes arbitrarily small.

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