Four-Dimensional Semi-Riemannian Szabó Manifolds

Abdoul Salam Diallo, Punam Gupta and Ljubisa Kocinac

Journal of Mathematics, 2020, vol. 2020, 1-5

Abstract: In this paper, we prove that the deformed Riemannian extension of any affine Szabó manifold is a Szabó pseudo-Riemannian metric and vice versa. We prove that the Ricci tensor of an affine surface is skew-symmetric and nonzero everywhere if and only if the affine surface is Szabó. We also find the necessary and sufficient condition for the affine Szabó surface to be recurrent. We prove that, for an affine Szabó recurrent surface, the recurrence covector of a recurrence tensor is not locally a gradient.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6663361

DOI: 10.1155/2020/6663361

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