A Warped Product Splitting Theorem Through Weak KAM Theory

TL;DR

This paper enhances the splitting theorem in differential geometry by applying weak KAM theory, offering a new perspective and strengthening previous results in the field.

Contribution

It introduces a novel approach to the splitting theorem using weak KAM theory, improving upon earlier proofs.

Findings

Strengthened the splitting theorem with new proof techniques

Connected weak KAM theory to geometric splitting results

Provided a more robust framework for geometric analysis

Abstract

In this paper, we strengthen the splitting theorem proved in [14, 15] and provide a different approach using ideas from the weak KAM theory.