A differentiable sphere theorem for compact Lagrangian submanifolds in complex Euclidean space and complex projective space

TL;DR

This paper presents a new differentiable sphere theorem specifically for compact Lagrangian submanifolds within complex Euclidean and projective spaces, advancing geometric understanding.

Contribution

It introduces a novel differentiable sphere theorem tailored for Lagrangian submanifolds in complex spaces, expanding the scope of geometric classification.

Findings

Establishes conditions under which Lagrangian submanifolds are diffeomorphic to spheres

Provides new criteria for differentiable sphere theorems in complex geometry

Enhances understanding of the topology of Lagrangian submanifolds

Abstract

We obtain a new differentiable sphere theorem for compact Lagrangian submanifolds in complex Euclidean space and complex projective space.