Cocalibrated G_2-manifolds with Ricci flat characteristic connection

TL;DR

This paper investigates 7-dimensional cocalibrated G_2-manifolds with a unique skew-symmetric torsion connection, focusing on cases where the Ricci tensor of this connection vanishes, revealing their geometric structure especially with many parallel vector fields.

Contribution

It characterizes the geometry of Ricci-flat characteristic connections on cocalibrated G_2-manifolds, especially with maximal parallel vector fields, advancing understanding of their structure.

Findings

Description of geometry with maximal parallel vector fields

Characterization of Ricci-flat characteristic connections

Insights into the structure of cocalibrated G_2-manifolds

Abstract

Any 7-dimensional cocalibrated G_2-manifold admits a unique connection $\nabla$ with skew symmetric torsion. We study these manifolds under the additional condition that the $\nabla$-Ricci tensor vanishes. In particular, we describe their geometry in case of a maximal number of $\nabla$-parallel vector fields.