On conformally flat LP-Sasakian manifolds with a coefficient \(\alpha\)
type: Item
instance of: scholarly article
title: On conformally flat LP-Sasakian manifolds with a coefficient \(\alpha\)
zbMATH Open document ID: 1035.53036
author: Uday Chand De
author: A. A. Shaikh
author: Jae-Bok Jun
published in: Nihonkai Mathematical Journal
publication date: 2002-01-01T00:00:00Z
review text: The notion of a Lorentzian almost paracontact manifold with a coefficient \(\alpha\) was introduced by \textit{U. C. De}, \textit{A. A. Shaikh} and \textit{A. Sengupta} [Kyungpook Math. J. 42, 177--186 (2002; Zbl 1022.53040)], a generalization of the Lorentzian almost paracontact manifold first introduced in 1989 by \textit{K. Matsumoto} [Bull. Yamagata Univ. Nat. Sci. 12, 151--156 (1989; Zbl 0675.53035)]. In the present paper the authors study a conformally flat LP-Sasakian manifold \(M_n\) with a coefficient \(\alpha\). It is shown that the characteristic vector field \(\xi\) is a concircular vector field if and only if \(M_n\) \((n> 3)\) is \(\eta\)-Einstein. Particularly, \(M_3\) is always an \(\eta\) Einstein manifold, if \(\alpha\) is constant. Moreover, \(M_n\) is of constant sectional curvature, if the scalar curvature is constant.
reviewed by: Demetra Demetropoulou-Psomopoulou
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 1932198
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1932198