Four-Dimensional Semi-Riemannian Szabó Manifolds. (31st December 2020)

• Record Type: Journal Article
• Authors: Diallo, Abdoul Salam; Gupta, Punam
• Other Names: Kocinac Ljubisa Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2020(2020)
• Publication Date: 2020-12-31
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2020/6663361
• Languages: English
• ISSNs: 2314-4629

Abstract

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.