Four-dimensional semi-Riemannian Szabó manifolds
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 proved 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.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2020
- DOI:
- 10.48550/arXiv.2010.06169
- arXiv:
- arXiv:2010.06169
- Bibcode:
- 2020arXiv201006169S
- Keywords:
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- Mathematics - Differential Geometry;
- 53B05;
- 53B20
- E-Print:
- arXiv admin note: text overlap with arXiv:1604.05424