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arXiv · 2505.16945

On a certain class of para-Hermite Einstein spaces

Adam Chudecki
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Abstract

A special class of (complex) para-Hermite Einstein spaces is analyzed. It is well-known that the self-dual Weyl tensor in para-Hermite Einstein spaces is of the Petrov-Penrose type [D]. In what follows we assume that the anti-self-dual Weyl tensor is algebraically degenerate. It is equivalent to the existence of an anti-self-dual congruence of null strings which is assumed not to be parallely propagated. Hence, spaces analyzed here are not Walker spaces. A classification of such spaces is given and the explicit metrics are found.

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Adam Chudecki. 2025-05-22. On a certain class of para-Hermite Einstein spaces. https://arxiv.org/abs/2505.16945

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