A note on para-holomorphic Riemannian Einstein manifolds
Differential Geometry
2016-10-12 v2
Abstract
The aim of this note is the study of Einstein condition for para-holomorphic Riemannian metrics in the para-complex geometry framework. Firstly, we make some general considerations about para-complex Riemannian manifolds (not necessarily para-holomorphic). Next, using an one-to-one correspondence between para-holomorphic Riemannian metrics and para-K\"ahler Norden metrics, we study the Einstein condition for a para-holomorphic Riemannian metric and the associated real para-K\"ahler Norden metric on a para-complex manifold. Finally, it is shown that every semi-simple para-complex Lie group inherits a natural para-K\"ahlerian Norden Einstein metric.
Cite
@article{arxiv.1507.01114,
title = {A note on para-holomorphic Riemannian Einstein manifolds},
author = {Cristian Ida and Alexandru Ionescu and Adelina Manea},
journal= {arXiv preprint arXiv:1507.01114},
year = {2016}
}
Comments
To appear in International Journal of Geometric Methods in Modern Physics