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

Year 2023, , 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

References

• [1] Anciaux, H., Panagiotidou, K.: Hopf hypersurfaces in pseudo-Riemannian complex and para-complex space forms. Diff. Geom. Appl. 42, 1-14 (2015).
• [2] Duggal, K. L., Bejancu, A.: ightlike Submanifolds of Semi-Riemannian Manifolds and Applications. Kluwer Acad. Publishers, Dordrecht (1996).
• [3] De Rham, G.: Sur la r´eductibilit´e d’un espace de Riemannian. Comm. Math. Helv., 26, 328-344 (1952).
• [4] Hayden, H. A.: Subspace of a space with torsion. Proc. London Math. Soc., 34, 27-50 (1932).
• [5] Jin, D. H.: Lightlike hypersurfaces of an indefinite generalized Sasakian space form with a symmetric metric connection of type (ℓ,m). Commun.Korean Math. Soc., 31 (3), 613-624 (2016).
• [6] Jin, D. H.: Lightlike hypersurfaces of an indefinite Kaehler manifold with a symmetric metric connection of type (ℓ,m). Bull. Korean Math. Soc., 53(4), 1171-1184 (2016).
• [7] Jin, D. H.: Special lightlike hypersurfaces of indefinite Kaehler manifolds. Filomat. 30 (7), 1919-1930 (2016).
• [8] Kimura, M., Ortega, M.: Hopf real hypersurfaces in the indefinite complex projective space. Mediterr. J. Math., 16:27 (2019).https://doi.org/10.1007/s00009-019-1299-9.
• [9] Yano, K.: On semi-symmetric metric connections. Rev. Roumaine Math. Pures Appl., 15, 1579-1586 (1970).
• [10] Yano, K., Imai, T.: Quarter-symmetric metric connection and their curvature tensors. Tensor, N.S., 38 (1982).