• East Asian mathematical journal
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• v.31 no.1
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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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• v.32 no.3
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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.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.483-500
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• 1997

We investigate the geometric properties reflected by the spectra of the Jacobi operator of a harmonic map when the target manifold is a Riemannian product manifold or a Kaehlerian product manifold. And also we study the spectral characterization of Riemannian sumersions when the target manifold is $S^n \times S^n$ or $CP^n \times CP^n$.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1457-1470
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• 2017

In this paper, we consider the stabilization of the viscoelastic wave equation with variable coefficients in a bounded domain with smooth boundary, subject to linear dissipative internal feedback with a delay. Our stabilization result is mainly based on the use of the Riemannian geometry methods and Lyapunov functional techniques.

• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.231-253
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• 2007

The purpose of this paper is to study the geometry of null curves in a semi-Riemannian manifold (M, g) of index 2. We show that it is possible to construct new Frenet equations of two types of null curves in M.

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.137-144
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• 1996

One of the fundamental problems in Riemannian geometry is "How the geometric invariants of Riemannian manifolds influenced by the curvature restriction \ulcorner".ner".uot;.

• Honam Mathematical Journal
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• v.31 no.1
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• pp.17-23
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• 2009

We study the geometry of screen conformal half lightlike submanifolds of a semi-Riemannian manifod. The main result is a classification theorem for screen conformal half lightlike submanifolds of a semi-Riemannian space form with a Killing co-screen distribution.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.763-770
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• 2012

In this paper, we study the geometry lightlike hypersurfaces (M, $g$, S(TM)) of a semi-Riemannian manifold ($\tilde{M}$, $\tilde{g}$) of quasi-constant curvature subject to the conditions: (1) The curvature vector field of $\tilde{M}$ is tangent to M, and (2) the screen distribution S(TM) is either totally geodesic in M or totally umbilical in $\tilde{M}$.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.717-732
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• 2006

In this paper, we study both slant 3nd semi-slant sub-manifolds of an almost product Riemannian manifold. We give characterization theorems for slant and semi-slant submanifolds and investigate special class of slant submanifolds which are product version of Kaehlerian slant submanifold. We also obtain integrability conditions for the distributions which are involved in the definition of a semi-slant submanifold. Finally, we prove a theorem on the geometry of leaves of distributions under a condition.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1255-1265
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• 2009

We show that the Riemannian geometry of a tangent sphere bundle of a Riemannian manifold (M, g) of constant radius $\gamma$ reduces essentially to the one of unit tangent sphere bundle of a Riemannian manifold equipped with the respective induced Sasaki metrics. Further, we provide some applications of this theorem on the $\eta$-Einstein tangent sphere bundles and certain related topics to the tangent sphere bundles.