On Hyperbolic F- Structure Manifold

Abstract

In this paper, we have defined Hyperbolic F-structure manifold and Hyperbolic metric F-structure manifold with some theorems
related to projection and rank. The integrability conditions for the manifold have been obtained and some related results are derived. We have defined Pseudo Projective curvature tensor W, Pseudo conformal curvature tensor C, Pseudo conharmonic curvature tensor L, Pseudo concircular curvature tensor V, Pseudo H-Projective curvature tensor P, Pseudo H-conharmonic curvature tensor S and Pseudo Bochner curvature tensor B in Hyperbolic F-structure manifold. Recurrence and Recurrence symmetry of different kinds have been defined and theorems of recurrent and recurrent symmetry of this manifold have been proved.