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In this paper we introduce the curvature tensors of (k,µ)-paracontact manifold satisfying the conditions R · W 0 = 0, P · W 0 = 0, e Z · W*0 = 0, e C · W 0 = 0 and W 0 · W 0 = 0. According these cases, (k, µ)-paracontact manifolds have been characterized such as -Einstein. [ABSTRACT FROM AUTHOR]

In this article, invariant submanifolds of Lorentz-Sasakian space forms on the W7- curvature tensor are investigated. For the W7-curvature tensor, the pseudoparallel, 2-pseudoparallel, Ricci generalized pesudoparallel and 2-Ricci generalized pseudoparallel properties of the invariant submanifolds of the Lorentz-Sasakian space form are discussed. [ABSTRACT FROM AUTHOR]

The object of this paper is to study the curvature tensors of (k; μ)-Paracontact manifold satisfying the conditions R(X; Y). C = 0, e Z(X; Y). C = 0 and C(X; Y). C = 0. According these cases, (k, μ)-Paracontact manifolds have been characterized such as Einstein and η-Einstein. [ABSTRACT FROM AUTHOR]

In this paper, we study the geometry of the contact pseudo-slant submanifolds of an (ε)--para Sasakian space form. We give some results for totally umbilical pseudo-slant submanifolds of an (ε)--para Sasakian manifolds and an (ε)--para Sasakian space forms. It is proved that such manifolds are η-Einstein. Finally, we have verified the theorems by providing an example of 5- dimensional proper contact pseudo-slant submanifold of ℝ9 with it's usual almost paracontact metric structure. [ABSTRACT FROM AUTHOR]

In this paper, we consider perfect fluid spacetime admitting (α, β)-type almost η-Ricci-Yamabe solitons by means of some curvature tensors. Ricci pseudosymmetry concepts of perfect fluid spacetime admitting (α, β)-type almost η-Ricci-Yamabe soliton are introduced according to the choice of some special curvature tensors such as Riemann, concircular and projective curvature tensor. After then, according to choosing of the curvature tensors, necessary conditions are given for perfect fluid spacetime admitting (α, β)-type almost η-Ricci-Yamabe soliton to be Ricci semisymmetric. Then, some important characterizations are given for Ricci, Yamabe, Einstein and η-Einstein solitons on perfect fluid spacetime. [ABSTRACT FROM AUTHOR]

The present paper deals with a study of doubly warped product contact CR-submanifolds of (LCS)n-manifolds and warped product contact CR-submanifolds of (LCS)n-manifolds. It is shown that there exists no doubly warped product contact CR-submanifolds of (LCS)n-manifolds. However, we obtain some results for the existence or non-existence of warped product contact CR-submanifolds of (LCS)n-manifolds and the existence is also ensured by an interesting example. [ABSTRACT FROM AUTHOR]