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arXiv · 2504.15221

On Walker and para-Hermite Einstein spaces

Adam Chudecki
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Abstract

A special class of (complex) para-Hermite Einstein spaces is analyzed. For this class of spaces the self-dual Weyl tensor is type-[D] in the Petrov-Penrose classification. The anti-self-dual Weyl tensor is algebraically degenerate, equivalently, there exists an anti-self-dual congruence of null strings. It is assumed that this congruence is parallely propagated. Thus, the spaces are not only para-Hermite but also Walker. A classification of the spaces according to three criteria is given. Finally, explicit metrics of all admitted Petrov-Penrose types are found.

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Adam Chudecki. 2025-04-21. On Walker and para-Hermite Einstein spaces. https://doi.org/10.1088/1751-8121%2Fae3d70

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