2013/02/08 by Shaikh, Absos Ali, Mondal, Chandan Kumar, Ahmad, Helaluddin
#53C15 #53C25 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1302.2139
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.