M-projectively flat Sasakian manifolds
type: Item
instance of: scholarly article
title: M-projectively flat Sasakian manifolds
zbMATH Open document ID: 0631.53038
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Let \(V_ n\) be a Sasakian manifold and M its M-projective curvature tensor. The author proves that \(V_ n\) is M-projectively flat if and only if it is an Einstein manifold (under the assumption that M is a recurrent tensor). The second important result of the paper states that the following three conditions are equivalent on a Sasakian manifold: (i) \(V_ n\) is M-projectively symmetric, (ii) \(V_ n\) is of constant curvature 1, (iii) \(R\circ R=0\) where the curvature transformation R acts on the tensor algebra as a derivation. We remark that a manifold satisfying the third condition is usually called a semi-symmetric space. These manifolds have been widely studied by \textit{I. Szabo} [J. Differ. Geom. 17, 531-582 (1982; Zbl 0508.53025)].
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 4026285
zbMATH Keywords: M-projective curvature tensor
zbMATH Keywords: Sasakian manifold
zbMATH Keywords: constant curvature
zbMATH Keywords: semi-symmetric space
author: R. H. Ojha
reviewed by: Liviu Ornea
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4026285