Mathematics and Statistics Vol. 8(3), pp. 286 - 292
DOI: 10.13189/ms.2020.080306
Reprint (PDF) (269Kb)

Lightlike Hypersurfaces of an Indefinite Kaehler Manifold with an ()-type Connection

Jae Won Lee ¹, Dae Ho Jin ², Chul Woo Lee ^3,*
1 Department of Mathematics Education and RINS, Gyeongsang National University, Jinju, 52828, Republic of Korea
² Department of Mathematics, Dongguk University, Gyeongju 38066, Republic of Korea
³ Department of Mathematics, Kyungpook National University, Daegu, 41566, Republic of Korea

ABSTRACT

Jin [1] defined an ()-type connection on semi-Riemannian manifolds. Semi-symmetric nonmetric connection and non-metric ∅-symmetric connection are two important examples of this connection such that () = (1; 0) and () = (0; 1), respectively. In semi-Riemannian geometry, there are few literatures for the lightlike geometry, so we expose new theories for non-degenerate submanifolds in semi-Riemannian geometry. The goal of this paper is to study a characterization of a (Lie) recurrent lightlike hypersurface M of an indefinite Kaehler manifold with an ()-type connection when the charateristic vector field is tangnet to M. In the special case that an indefinite Kaehler manifold of constant holomorphic sectional curvature is an indefinite complex space form, we investigate a lightlike hypersurface of an indefinite complex space form with an ()-type connection when the charateristic vector field is tangnet to M. Moreover, we show that the total space, the complex space form, is characterized by the screen conformal lightlike hypersurface with an ()-type connection. With a semi-symmetric non-metric connection, we show that an indefinite complex space form is flat.

KEYWORDS
Compound Non-symmetric Non-metric Connection, Lightlike Hypersurface, Indefinite Kaehler Manifold, Indefinite Complex Space Form

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Jae Won Lee , Dae Ho Jin , Chul Woo Lee , "Lightlike Hypersurfaces of an Indefinite Kaehler Manifold with an ()-type Connection," Mathematics and Statistics, Vol. 8, No. 3, pp. 286 - 292, 2020. DOI: 10.13189/ms.2020.080306.

(b). APA Format:
Jae Won Lee , Dae Ho Jin , Chul Woo Lee (2020). Lightlike Hypersurfaces of an Indefinite Kaehler Manifold with an ()-type Connection. Mathematics and Statistics, 8(3), 286 - 292. DOI: 10.13189/ms.2020.080306.