Lightlike Hypersurfaces of an Indefinite Kaehler Manifold with an $(\ell,\,m)$-type Metric Connection

Year 2023, Volume: 16 Issue: 2, 526 - 538, 29.10.2023

Dae Ho Jin , Chul Woo Lee , Jae Won Lee

https://doi.org/10.36890/iejg.1264249

Abstract

Jin introduced a non-symmetric metric connection, called an {\it $(\ell,m)$-type metric connection} \cite{Jin1, Jin2}.
There are two examples of $(\ell, m)$-type: a semi-symmetric metric connection when ${\ell}=1$ and $m=0$ and a quater-symmetric connection for ${\ell}=0$ and $m=1$ . Our purpose is to investigate lightlike hypersurfaces of an indefinite (complex) Kaehler manifolds with an $(\ell,m)$-type metric connection under the tangent characteristic vector field on such hypersurfaces.

Keywords

$(\ell¸m)$-type metric connection, lightlike hypersurface, indefinite Kaehler manifold

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