- Hacettepe Journal of Mathematics and Statistics
- Vol: 48 Issue: 4
- On locally $\phi$-semisymmetric Sasakian manifolds
On locally $\phi$-semisymmetric Sasakian manifolds
Authors : Absos Ali Shaikh, Chandan Kumar Mondal, Helaluddin Ahmad
Pages : 1156-1169
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Publication Date : 2019-08-08
Article Type : Research
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