A topological sphere theorem for submanifolds of the hyperbolic space

TL;DR

This paper characterizes certain complete submanifolds in hyperbolic space as topological spheres based on Ricci curvature bounds related to their mean curvature vector.

Contribution

It establishes a topological sphere theorem for submanifolds in hyperbolic space using Ricci curvature bounds dependent on mean curvature.

Findings

Complete submanifolds with Ricci curvature bounds are topological spheres.

The Ricci curvature lower bound depends solely on the mean curvature vector.

The result applies to submanifolds of any codimension in hyperbolic space.

Abstract

We identify as topological spheres those complete submanifolds lying with any codimension in hyperbolic space whose Ricci curvature satisfies a lower bound contingent solely upon the length of the mean curvature vector of the immersion.