On locally phi-semisymmetric Sasakian manifolds

Abstract

Generalizing the notion of local $\varphi$-symmetry of Takahashi, in the present paper, we introduce the notion of local $\varphi$-semisymmetry of a Sasakian manifold along with its proper existence and characterization. We also study the notion of local Ricci (resp., projective, conformal) $\varphi$-semisymmetry of a Sasakian manifold and obtain its characterization. It is shown that the local $\varphi$-semisymmetry, local projective $\varphi$-semisymmetry and local concircular $\varphi$-semisymmetry are equivalent. It is also shown that local conformal $\varphi$-semisymmetry and local conharmonical $\varphi$-semisymmetry are equivalent.

20 pages, Any suggestion and comments are appreciated