Absos Ali SHAİKH, Chandan Kumar MONDAL, Helaluddin AHMAD

On locally $\phi$-semisymmetric Sasakian manifolds

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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Hacettepe Journal of Mathematics and Statistics-Cover

Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

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