Non-symmetric Riemannian gravity and Sasaki-Einstein 5-manifolds
Differential Geometry
2020-01-29 v1
Abstract
We show that a connection with skew-symmetric torsion satisfying the Einstein metricity condition exists on an almost contact metric manifold exactly when it is D-homothetic to a cosymplectic manifold. In dimension five, we get that the existence of a connection with skew torsion satisfying the Einstein metricity condition is equivalent to the existence of a Sasaki-Einstein 5-manifold and vice versa, any Sasaki-Einstein 5-manifold generates a two parametric family of connections with skew torsion satisfying the Einstein metricity condition. Formulas for the curvature and the Ricci tensors of these connections are presented in terms of the Sasaki-Einstein SU(2) structures.
Keywords
Cite
@article{arxiv.1905.04013,
title = {Non-symmetric Riemannian gravity and Sasaki-Einstein 5-manifolds},
author = {Stefan Ivanov and Milan Zlatanović},
journal= {arXiv preprint arXiv:1905.04013},
year = {2020}
}