• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2089-2101
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• 2013

The aim of this paper is to introduce the notion of Lie recurrent structure Jacobi operator for real hypersurfaces in non-flat complex space forms and to study such real hypersurfaces. More precisely, the non-existence of such real hypersurfaces is proved.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.101-115
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• 2017

In this paper, we study three types of lightlike hypersurfaces, which are called recurrent, Lie recurrent and Hopf lightlike hypersurfaces, of an indefinite Kaehler manifold with a semi-symmetric non-metric connection. We provide several new results on such three types of lightlike hypersurfaces of an indefinite Kaehler manifold or an indefinite complex space form, with a semi-symmetric non-metric connection.

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.223-238
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• 2020

We study a lightlike hypersurface M of an indefinite nearly trans-Sasakian manifold ${\bar{M}}$ with an (ℓ, m)-type connection such that the structure vector field ζ of ${\bar{M}}$ 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.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.619-632
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• 2017

We define a new connection on semi-Riemannian manifold, which is called a non-metric ${\phi}$-symmetric connection. Semi-symmetric non-metric connection and quarter-symmetric non-metric connection are two impotent examples of this connection. The purpose of this paper is to study the geometry of lightlike hypersurfaces of an indefinite Kaehler manifold with a non-metric ${\phi}$-symmetric connection.