This study presents a study of concircular structure spacetimes which are connected 4-dimensional Lorentzian concircular structure manifolds

We studied concircular structure spacetimes which are connected 4-dimensional Lorentzian concircular structure manifolds.2000 Mathematics subject classification: 53C40, 53C50, 53C80

Abstract. The object of the present paper is to provide the existence of LP-Sasakian manifolds with η-recurrent, η-parallel, φ-recurrent, φ-parallel Ricci tensor with several non-trivial examples. Also generalized Ricci recurrent LP-Sasakian manifolds are studied with the existence of various examples.

The purpose of this paper is to introduce the notions of an almost generalized weakly symmetric LP-Sasakian manifolds and an almost generalized weakly Ricci-symmetric LP-Sasakian manifolds. The existence of an almost generalized weakly symmetric LP-Sasakian manifold is ensured by a non-trivial example.

Abstract. The object of the present paper is to study a transformation called Dhomothetic deformation of trans-Sasakian structure. Among others it is shown that in a trans-Sasakian manifold, the Ricci operator Q does not commute with the structure tensor φ and the operator Qφ − φQ is conformal under a D-homothetic deformation. Also the φ-sectional curvature of a trans-Sasakian manifold is conformal under such a deformation. Some non-trivial examples of trans-Sasakian (non-Sasakian) manifolds with global vector fields are obtained. IntroductionA. Trans-Sasakian structure Let V be a 2n-dimensional C ∞ -almost Hermitian manifold with metric g and almost complex structure J. The Kähler form Ω is defined by Ω(X, Y ) = g(X, JY ) for all X, Y ∈ χ(V ), χ(V ) being the Lie algebra of C ∞ vector fields on V . Then V is said to be Kähler if dΩ = 0 and N J = 0, where N J denotes Nijenhuis tensor of J. Also V is called locally conformal Kähler if its metric is conformally related to a Kähler metric in some neighbourhood of every point of V .Let M be a (2n+1)-dimensional C ∞ -almost contact metric manifold with metric g and almost contact metric structure (φ, ξ, η, g). Then we have (1.1)for X, Y ∈ χ(M ), where I denotes the identity transformation and ⊗ denotes the tensor product. The fundamental 2-form Φ of the almost contact metric 1991 Mathematics Subject Classification: 53C15, 53C25.