A generalized sphere theorem and its applications

TL;DR

This paper establishes a generalized sphere theorem for compact Riemannian manifolds with bounded radial Ricci curvature, expanding the understanding of geometric structures under curvature constraints.

Contribution

The paper introduces a new generalized sphere theorem applicable to manifolds with radial Ricci curvature bounds, extending classical results in Riemannian geometry.

Findings

Proves a generalized sphere theorem for specific curvature conditions

Provides new geometric insights into Riemannian manifolds with bounded radial Ricci curvature

Extends classical sphere theorems to broader curvature settings

Abstract

In this paper, we successfully set up a generalized sphere theorem for compact Riemannian manifolds with radial Ricci curvature bounded.