Bismut connection on Vaisman manifolds

Abstract

The holonomy of the Bismut connection on Vaisman manifolds is studied. We prove that if $M^{2n}$ is endowed with a Vaisman structure, then the holonomy group of the Bismut connection is contained in U$(n-1)$. We compute explicitly this group for particular types of manifolds, namely, solvmanifolds and some classical Hopf manifolds.

38 pages