Einstein four-manifolds with skew torsion

TL;DR

This paper introduces Einstein manifolds with skew torsion in four dimensions, establishing inequalities and exploring moduli spaces of instantons, thereby extending classical geometric concepts with torsion considerations.

Contribution

It develops a new framework for Einstein manifolds with skew torsion in four dimensions and analyzes their geometric and topological properties, including moduli space structure.

Findings

Proves an analogue of the Hitchin-Thorpe inequality for these manifolds.

Studies the case of equality in the inequality.

Examines the moduli space of 1-instantons on the 4-sphere.

Abstract

We develop a notion of Einstein manifolds with skew torsion on compact, orientable Riemannian manifolds of dimension four. We prove an analogue of the Hitchin-Thorpe inequality and study the case of equality. We use the link with self-duality to study the moduli space of 1-instantons on the 4-sphere for a family of metrics defined by Bonneau.