A modified Yamabe invariant and a Hopf conjecture

TL;DR

This paper introduces new curvature invariants for 4-manifolds and explores their connection to the Hopf conjecture, advancing understanding of geometric properties in differential geometry.

Contribution

It defines bi-orthogonal sectional curvature and two modified Yamabe invariants, linking one invariant to the Hopf conjecture in 4-dimensional geometry.

Findings

Established a relationship between a modified Yamabe invariant and the Hopf conjecture.

Introduced bi-orthogonal sectional curvature for 4-manifolds.

Proposed two new invariants related to curvature and topology.

Abstract

In this paper we define the bi-orthogonal sectional curvature and we present two modified Yamabe invariants for compact 4-dimensional manifolds. In particular we obtained a relationship between one of these invariants and a Hopf conjecture.