Some characterizations of three-dimensional trans-Sasakian manifolds admitting η- Ricci solitons and trans-Sasakian manifolds as Kagan subprojective space

Abstract

UDC 514.7 The object of the present paper is to study three-dimensional trans-Sasakian manifolds admittingη-Ricci soliton. Actually, we study such manifolds whose Ricci tensor satisfy some special conditions like cyclic parallelity, Ricci semisymmetry,ϕ-Ricci semisymmetry, after reviewing the properties of second order parallel tensors on such manifolds. We determine the form of Riemann curvature tensor of trans-Sasakian manifolds of dimension greater than three as Kagan subprojective spaces. We also give some classification results of trans-Sasakian manifolds of dimension greater than three as Kagan subprojective spaces.