Four-dimensional manifolds with degenerate self-dual Weyl curvature operator |
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| Authors: | Alexandre Cortés-Ayaso J Carlos Díaz-Ramos Eduardo García-Río |
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| Institution: | (1) Faculty of Mathematics, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain;(2) Department of Mathematics, University College Cork, Cork, Ireland |
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| Abstract: | It is shown that any four-dimensional Walker metric of nowhere zero scalar curvature has a natural almost para-Hermitian structure.
In contrast to the Goldberg–Sachs theorem, if this structure is self-dual and *-Einstein, it is symplectic but not necessarily
integrable. This is due to the non-diagonalizability of the self-dual Weyl conformal curvature tensor.
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| Keywords: | Para-Hermitian and para-K?hler structure Self-dual Weyl curvature tensor Walker metric |
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