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Kyungpook Mathematical Journal 2020; 60(2): 223-238

Published online June 30, 2020

Copyright © Kyungpook Mathematical Journal.

Lightlike Hypersurfaces of an Indefinite Nearly Trans-Sasakian Manifold with an (ℓ,m)-type Connection

Chul Woo Lee, Jae Won Lee∗

Department of Mathematics, Kyungpook National University, Daegu 41566, Korea
e-mail : mathisu@knu.ac.kr
Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 52828, Korea
e-mail : leejaew@gnu.ac.kr

Received: February 14, 2020; Revised: March 31, 2020; Accepted: April 27, 2020

Abstract

We study a lightlike hypersurface M of an indefinite nearly trans-Sasakian manifold M- with an (ℓ,m)-type connection such that the structure vector field ζ of M- is tangent to M. In particular, we focus on such lightlike hypersurfaces M for which the structure tensor field F is either recurrent or Lie recurrent, or such that M itself is totally umbilical or screen totally umbilical.

Keywords: (ℓ,m)-type connection, recurrent, Lie recurrent, lightlike hypersurface, indefi,nite nearly trans-Sasakian manifold.