Extrinsic Bonnet-Myers Theorem and almost rigidity

TL;DR

This paper extends the classical Bonnet-Myers theorem to extrinsic settings and demonstrates an almost rigidity result for hypersurfaces with positive sectional curvature and near-maximal extrinsic diameter.

Contribution

It introduces an extrinsic version of the Bonnet-Myers theorem and proves an almost rigidity theorem for certain hypersurfaces in Euclidean space.

Findings

Established the extrinsic Bonnet-Myers theorem for compact manifolds with positive Ricci curvature.

Proved almost rigidity for hypersurfaces with positive sectional curvature and near-maximal extrinsic diameter.

Extended classical intrinsic results to extrinsic geometric contexts.

Abstract

We establish the extrinsic Bonnet-Myers Theorem for compact Riemannian manifolds with positive Ricci curvature. And we show the almost rigidity for compact hypersurfaces, which have positive sectional curvature and almost maximal extrinsic diameter in Euclidean space.