(k,μ)-Paracontact Manifolds and Their Curvature Classification
Abstract
The aim of this paper is to study (k,μ)-Paracontact metric manifold. We introduce the curvature tensors of a (k,μ)-paracontact metric manifold satisfying the conditions R⋅P_*=0, R⋅L=0, R⋅W_1=0, R⋅W_0=0 and R⋅M=0. According to these cases, (k,μ)-paracontact manifolds have been characterized such as η-Einstein and Einstein. We get the necessary and sufficient conditions of a (k,μ)-paracontact metric manifold to be η-Einstein. Also, we consider new conclusions of a (k,μ)-paracontact metric manifold contribute to geometry. We think that some interesting results on a (k,μ)-paracontact metric manifold are obtained.
Keywords
(k, μ)-Paracontact manifold, η-Einstein manifold, Riemannian curvature tensor.
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