A counterexample to Belgun-Moroianu conjecture

TL;DR

This paper presents a specific counterexample to the Belgun-Moroianu conjecture, demonstrating a closed manifold with a nonflat, reducible, locally metric connection that preserves a conformal structure but is not a Levi-Civita connection.

Contribution

The authors construct a novel counterexample disproving the Belgun-Moroianu conjecture by explicitly exhibiting a manifold with unique geometric properties.

Findings

Counterexample to the Belgun-Moroianu conjecture

Existence of a closed manifold with a special connection

Demonstration of a non-Levi-Civita, conformally preserving connection

Abstract

We construct an example of a closed manifold with a nonflat reducible locally metric connection such that it preserves a conformal structure and such that it is not the Levi-Civita connection of a Riemannian metric.