On locally phi-semisymmetric Sasakian manifolds

英文摘要：

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