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.
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
Primary Language | English |
---|---|
Subjects | Mathematical Sciences |
Journal Section | Mathematics |
Authors | |
Publication Date | August 8, 2019 |
Published in Issue | Year 2019 Volume: 48 Issue: 4 |