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arXiv · 1507.01114

A note on para-holomorphic Riemannian Einstein manifolds

Cristian Ida·Alexandru Ionescu·Adelina Manea
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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-Kähler Norden metrics, we study the Einstein condition for a para-holomorphic Riemannian metric and the associated real para-Kähler Norden metric on a para-complex manifold. Finally, it is shown that every semi-simple para-complex Lie group inherits a natural para-Kählerian Norden Einstein metric.

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Cristian Ida, Alexandru Ionescu, Adelina Manea. 2016-05-19. A note on para-holomorphic Riemannian Einstein manifolds. https://doi.org/10.1142/s0219887816501073

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