Flag Foliations Functionals. The Hopf Hypothesis

TL;DR

This paper introduces a novel class of functionals to analyze manifolds diffeomorphic to S^2×S^2 and successfully addresses the long-standing Hopf conjecture using these tools.

Contribution

It presents a new type of functionals and applies them to prove the Hopf conjecture for specific manifolds, advancing geometric analysis methods.

Findings

Established the Hopf conjecture for S^2×S^2 manifolds

Developed a new class of functionals for manifold analysis

Provided new insights into the geometry of product manifolds

Abstract

With the help of a new type of functionals we study manifolds diffeomorphic to $S^2\times S^2$ and establish, in particular, the Hopf conjecture.