On Kenmotsu manifolds admitting a special type of semi-symmetric non-metric $\phi-$ connection
Novi Sad Journal of Mathematics, Tome 48 (2018) no. 1.

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The object of the present paper is to study a special type of semi-symmetric non-metric $\phi$-connection on a Kenmotsu manifold. It is shown that if the curvature tensor of Kenmotsu manifolds admitting a special type of semi-symmetric non-metric $\phi$-connection $\bar{\nabla}$ vanishes, then the Kenmotsu manifold is locally isometric to the hyperbolic space $H^n(-1)$. Beside these, we consider Weyl conformal curvature tensor of a Kenmotsu manifold with respect to the semi-symmetric non-metric $\phi$-connection. Among other results, we prove that the Weyl conformal curvature tensor with respect to the Levi-Civita connection and the semi-symmetric non-metric $\phi$-connection are equivalent. Moreover, we deal with $\phi$-Weyl semi-symmetric Kenmotsu manifolds with respect to the semi-symmetric non-metric $\phi$-connection. Finally, an illustrative example is given to verify our result.
Publié le :
DOI : 10.30755/NSJOM.06311
Classification : 53C15, 53C25
Keywords: Kenmotsu manifold, semi-symmetric non-metric $\phi$-connection, Weyl conformal curvature tensor, $\phi$-Weyl semi-symmetric, Levi-Civita connection
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     title = {On  {Kenmotsu}  manifolds admitting a special type of semi-symmetric non-metric $\phi-$ connection},
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     pages = {47 - 60},
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Ajit Barman; Uday Chand De; Pradip Majhi. On  Kenmotsu  manifolds admitting a special type of semi-symmetric non-metric $\phi-$ connection. Novi Sad Journal of Mathematics, Tome 48 (2018) no. 1. doi : 10.30755/NSJOM.06311. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.06311/

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