Paracontact Metric (k; μ )-spaces Satisfying Certain Curvature Conditions
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The object of this paper is to classify paracontact metric (k; μ )-spaces satisfying certain curvature conditions. We show that a paracontact metric (k; μ )-space is Ricc emisymmetric if and only if the metric is Einstein, provided k < -1. Also we prove that a paracontact metric (k;μ )-space is -Ricci symmetric if and only if the metric is Einstein, provided k = /0, -1. Moreover, we show that in a paracontact metric (k;μ )-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.
Abstract
The object of this paper is to classify paracontact metric (k; μ )-spaces satisfying certain curvature conditions. We show that a paracontact metric (k; μ )-space is Ricc emisymmetric if and only if the metric is Einstein, provided k < -1. Also we prove that a paracontact metric (k;μ )-space is -Ricci symmetric if and only if the metric is Einstein, provided k = /0, -1. Moreover, we show that in a paracontact metric (k;μ )-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.
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