A remark on the reach and upper bounds on some extrinsic geometry invariants of submanifolds

Reza Mirzaie

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arXiv · 2503.07054

A remark on the reach and upper bounds on some extrinsic geometry invariants of submanifolds

Reza Mirzaie

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Abstract

We consider a compact submanifold $M$ of a Riemannian manifold $N$ and we use the second variation formula as a tool to drive some geometric results on reach$(M, N)$ the reach of $M$ in $N$, including some useful relations between the extrinsic geometry of $M$ in $N$ and reach$(M, N)$. Our results generalize some theorems previously proved for the special case where $N$ is Euclidean space.

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Reza Mirzaie. 2025-03-10. A remark on the reach and upper bounds on some extrinsic geometry invariants of submanifolds. https://arxiv.org/abs/2503.07054

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