• 대한수학회논문집
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• 제27권4호
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• pp.781-793
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• 2012

We study some properties of a semi-Riemannian submanifold of a semi-Riemannian manifold with a semi-symmetric non-metric connection. Then, we prove that the Ricci tensor of a semi-Riemannian submanifold of a semi-Riemannian space form admitting a semi-symmetric non-metric connection is symmetric but is not parallel. Last, we give the conditions under which a totally umbilical semi-Riemannian submanifold with a semi-symmetric non-metric connection is projectively flat.

• 충청수학회지
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• 제22권4호
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• pp.653-665
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• 2009

We define a semi-symmetric non-metric connection in an almost r-paracontact Riemannian manifold and we consider submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric non-metric connection and obtain Gauss and Codazzi equations, Weingarten equation and curvature tensor for submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric non-metric connection.

• East Asian mathematical journal
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• 제31권1호
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• pp.33-40
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• 2015

We study the geometry of r-lightlike submanifolds M of a semi-Riemannian manifold $\bar{M}$ with a semi-symmetric non-metric connection subject to the conditions; (a) the screen distribution of M is totally geodesic in M, and (b) at least one among the r-th lightlike second fundamental forms is parallel with respect to the induced connection of M. The main result is a classification theorem for irrotational r-lightlike submanifold of a semi-Riemannian manifold of index r admitting a semi-symmetric non-metric connection.

• Korean Journal of Mathematics
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• 제32권3호
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• pp.407-424
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• 2024

The present work aims to introduce the geometry of invariant and screen semi-invariant lightlike submanifolds of a metallic semi-Riemannian manifold equipped with a quarter symmetric non-metric connection. The study establishes the characterization of integrability and parallelism of the distributions inherent in these submanifolds. Additionally, the conditions for distributions defining totally geodesic foliations on the invariant and screen semi-invariant lightlike submanifolds of metallic semi-Riemannian manifold are specified.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권3호
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• pp.211-228
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• 2012

We study lightlike submanifolds M of a semi-Riemannian manifold $\bar{M}$ with a semi-symmetric non-metric connection subject to the conditions; (a) the characteristic vector field of $\bar{M}$ is tangent to M, (b) the screen distribution on M is totally umbilical in M and (c) the co-screen distribution on M is conformal Killing.

• 대한수학회보
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• 제47권5호
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• pp.1089-1103
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• 2010

In this paper, we study lightlike submanifolds of a semi-Riemannian manifold admitting a semi-symmetric non-metric connection. We obtain a necessary and a sufficient condition for integrability of the screen distribution. Then we give the conditions under which the Ricci tensor of a lightlike submanifold with a semi-symmetric non-metric connection is symmetric. Finally, we show that the Ricci tensor of a lightlike submanifold of semi-Riemannian space form is not parallel with respect to the semi-symmetric non-metric connection.

• 대한수학회보
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• 제46권5호
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• pp.895-903
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• 2009

We define a semi-symmetric metric connection in an almost $\gamma$-paracontact Riemannian manifold and we consider invariant, non-invariant and anti-invariant hypersurfaces of an almost $\gamma$-paracontact Riemannian manifold endowed with a semi-symmetric metric connection.

• 대한수학회지
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• 제51권2호
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• pp.311-323
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• 2014

In this paper, we construct two types of non-tangential half lightlike submanifolds of a semi-Riemannian manifold admitting a semi-symmetric non-metric connection. Our main result is to prove several characterization theorems for each types of such half lightlike submanifolds equipped with totally geodesic screen distributions.

• 대한수학회논문집
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• 제38권4호
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• pp.1233-1247
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• 2023

The aim of the present paper is to study complete lifts of a semi-symmetric non-metric connection from a Riemannian manifold to its tangent bundles. Some curvature properties of a Riemannian manifold to its tangent bundles with respect to such a connection have been investigated.

• 대한수학회보
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• 제54권2호
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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.