Sphere theorems for submanifolds in K\"ahler Manifold

TL;DR

This paper establishes new differentiable and topological sphere theorems for submanifolds within Kähler manifolds, particularly focusing on complex space forms, advancing understanding of their geometric and topological properties.

Contribution

It introduces novel sphere theorems specifically for submanifolds in Kähler manifolds, especially in complex space forms, expanding the scope of classical sphere theorems.

Findings

Proved differentiable sphere theorems for submanifolds in Kähler manifolds.

Established topological sphere theorems in the context of complex space forms.

Extended classical sphere theorems to the setting of Kähler geometry.

Abstract

In this paper, we prove some differentiable sphere theorems and topological sphere theorems for submanifolds in K\"ahler manifold, especially in complex space forms.