Four-dimensional manifolds with positive biorthogonal curvature

TL;DR

This paper classifies all simply-connected 4-manifolds that can have a metric with positive biorthogonal curvature, expanding understanding of curvature conditions in four-dimensional geometry.

Contribution

It provides a classification of 4-manifolds admitting metrics with positive biorthogonal curvature, a new curvature condition in differential geometry.

Findings

Classification of such 4-manifolds up to homeomorphism

Identification of geometric constraints for positive biorthogonal curvature

Extension of curvature condition understanding in 4D manifolds

Abstract

We classify, up to homeomorphisms, the closed simply-connected 4-manifolds that admit a Riemannian metric for which averages of pairs of sectional curvatures of orthogonal planes are positive.