• 대한수학회논문집
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• 제35권4호
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• pp.1255-1267
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• 2020

The class of isotropic almost complex structures, J_𝛿,𝜎, define a class of Riemannian metrics, g_𝛿,𝜎, on the tangent bundle of a Riemannian manifold which are a generalization of the Sasaki metric. This paper characterizes the metrics g_𝛿,0 using the geometry of tangent bundle. As a by-product, some integrability results will be reported for J_𝛿,𝜎.

• 대한수학회지
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• 제34권2호
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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 $CP^n \times CP^n$.

• 대한수학회보
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• 제54권4호
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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.

• 대한수학회지
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• 제33권1호
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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;.

• 대한수학회논문집
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• 제37권3호
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• pp.865-879
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• 2022

Let (M^m, g) be an m-dimensional Riemannian manifold. In this paper, we introduce a new class of metric on (M^m, g), obtained by a non-conformal deformation of the metric g. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. In the last section we characterizes some class of proper biharmonic maps. Examples of proper biharmonic maps are constructed when (M^m, g) is an Euclidean space.

• 대한수학회지
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• 제46권6호
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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.

• 대한수학회논문집
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• 제27권4호
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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 $\tilde{M}$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권4호
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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.

• 호남수학학술지
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• 제31권1호
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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.

• 대한수학회지
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• 제43권4호
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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.