Infinite families of homogeneous Bismut Ricci flat manifolds

TL;DR

This paper constructs infinite families of compact homogeneous spaces with invariant Bismut connections that are Ricci flat, generalizing symmetric spaces and their embeddings into Lie groups.

Contribution

It introduces new infinite families of homogeneous Bismut Ricci flat manifolds derived from symmetric spaces, extending the Cartan embedding framework.

Findings

Examples are generalized symmetric spaces of order 4.

These manifolds can be realized as minimal submanifolds of Bismut flat spaces.

The construction provides new instances of Ricci flat Bismut connections on compact homogeneous spaces.

Abstract

Starting from compact symmetric spaces of inner type, we provide infinite families of compact homogeneous spaces carrying invariant non-flat Bismut connections with vanishing Ricci tensor. These examples turn out to be generalized symmetric spaces of order $4$ and (up to coverings) can be realized as minimal submanifolds of the Bismut flat model spaces, namely compact Lie groups. This construction generalizes the standard Cartan embedding of symmetric spaces.