[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2019.59.1.163

Paracontact Metric (k, 𝜇)-spaces Satisfying Certain Curvature Conditions

Mandal, Krishanu (Department of Pure Mathematics, University of Calcutta)
De, Uday Chand (Department of Pure Mathematics, University of Calcutta)

Publication Information

Kyungpook Mathematical Journal / v.59, no.1, 2019 , pp. 163-174 More about this Journal

Abstract

The object of this paper is to classify paracontact metric ( $k,{\mu}$ )-spaces satisfying certain curvature conditions. We show that a paracontact metric ( $k,{\mu}$ )-space is Ricci semisymmetric if and only if the metric is Einstein, provided k < -1. Also we prove that a paracontact metric ( $k,{\mu}$ )-space is ${\phi}$ -Ricci symmetric if and only if the metric is Einstein, provided $k{\neq}0$ , -1. Moreover, we show that in a paracontact metric ( $k,{\mu}$ )-space with k < -1, a second order symmetric parallel tensor is a constant multiple of the associated metric tensor. Several consequences of these results are discussed.

Keywords

paracontact metric ( $k,{\mu}$ )-spaces; Ricci semisymmetric; ${\phi}$ -Ricci symmetry; second order parallel tensor; Einstein manifold;

Citations & Related Records

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