On locally $\phi$-semisymmetric Sasakian manifolds

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 (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

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