• 대한수학회보
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• 제50권3호
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• pp.951-962
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• 2013

We introduce semi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalization of slant submersions, semi-invariant submersions, anti-invariant submersions, etc. We obtain characterizations, investigate the integrability of distributions and the geometry of foliations, etc. We also find a condition for such submersions to be harmonic. Moreover, we give lots of examples.

• 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.

• 호남수학학술지
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• 제34권2호
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• pp.231-239
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• 2012

In this paper, we obtain the Ricci curvature and the scalar curvature on SU(3) with some left invariant Riemannian metric. And then we get a necessary and sufficient condition for the scalar curvature (resp. the Ricci curvature) on the Riemannian manifold SU(3) to be positive.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권4호
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• pp.309-321
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• 2004

For a complete open Riemannian manifold, the ideal boundary consists of points at infinity. The so-called Busemann-functions play the role of distance functions for points at infinity. We study the similarity and difference between Busemann-functions and ordinary distance functions.

• 충청수학회지
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• 제28권2호
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• pp.229-241
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• 2015

In this paper, we decompose the curvature tensor (field) on the homogeneous Riemannian manifold SU(3)=T (k, l) with an arbitrarily given SU(3)-invariant Riemannian metric into three curvature-like tensor fields, and investigate geometric properties.

• Journal of applied mathematics & informatics
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• 제36권5_6호
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• pp.521-530
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• 2018

Several classes of functions, named as semi E-preinvex functions and semilocal E-preinvex functions and their properties are studied by various authors. In this paper we introduce the geodesic concept over two types of problems first is semi E-preinvex functions and another is semilocal E-preinvex functions on Riemannian manifolds and study some of their properties.

• 대한수학회논문집
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• 제10권2호
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• pp.357-363
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• 1995

We study non-existence of $L^2$-harmonic p-forms on a complete, non-compact Riemannian manifold without boundary as extension of results of K. Yano in the case of compact.

• 대한수학회논문집
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• 제31권3호
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• pp.647-656
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• 2016

In this paper, we define the generalized golden shaped hypersurfaces in Lorentz space forms. Based on the classification of proper semi-Riemannian hypersurfaces in semi-Riemannian real space forms, we obtain the whole families of the generalized golden shaped hypersurfaces in Lorentz space forms.

• 대한수학회지
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• 제43권1호
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• pp.133-145
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• 2006

We study Riemannian or pseudo-Riemannian manifolds which admit a closed conformal vector field. Subject to the condition that at each point $p{\in}M^n$ the set of conformal gradient vector fields spans a non-degenerate subspace of TpM, using a warped product structure theorem we give a complete description of the space of conformal vector fields on arbitrary non-Ricci flat Einstein spaces.

• 대한수학회지
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• 제54권5호
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• pp.1441-1456
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• 2017

We consider a 3-dimensional Riemannian manifold M with a circulant metric g and a circulant structure q satisfying $q^3=id$. The structure q is compatible with g such that an isometry is induced in any tangent space of M. We introduce three classes of such manifolds. Two of them are determined by special properties of the curvature tensor. The third class is composed by manifolds whose structure q is parallel with respect to the Levi-Civita connection of g. We obtain some curvature properties of these manifolds (M, g, q) and give some explicit examples of such manifolds.