On locally $\phi$-semisymmetric Sasakian manifolds

Authors : Absos Ali SHAİKH, Chandan Kumar MONDAL, Helaluddin AHMAD

Pages : 1156-1169

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Publication Date : 2019-08-08

Article Type : Research Paper

Abstract :Generalizing the notion of local $\phi$-symmetry of Takahashi [Sasakian $\phi$-symmetric spaces, Tohoku Math. J., 1977], in the present paper, we introduce the notion of  \textit{local $\phi$-semisymmetry} of a Sasakian manifold along with its proper existence and characterization. We also study the notion of  local Ricci insert ignore into journalissuearticles values(resp., projective, conformal); $\phi$-semisymmetry of a  Sasakian manifold and obtain its characterization. It is shown that the local $\phi$-semisymmetry, local projective $\phi$-semisymmetry and local concircular $\phi$-semisymmetry are equivalent. It is also shown that local conformal $\phi$-semisymmetry and local conharmonical $\phi$-semisymmetry are equivalent.
Keywords : Sasakian manifold, locally phi symmetric, phi semisymmetric, Ricci phi semisymmetric, projectively phi semisymmetric, conformally phi semisymmetric, manifold of constant curvature, B tensor, B phi semisymmetric