• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.237-249
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• 2002

We study nondegenerate immersions of Riemannian manifolds of constant sectional curvatures into Lorentzian manifolds of the same constant sectional curvatures with flat normal bundles. We also give a method to produce such immersions using the so-called Grassmannian system. .

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.787-799
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• 2013

In this paper, we compute the sectional curvatures and the scalar curvature of the Siegel-Jacobi space $\mathb{H}_1{\times}\mathb{C}$ of degree 1 and index 1 explicitly.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.295-310
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• 2014

This paper provides a study of lightlike submanifolds of a generalized Robertson-Walker (GRW) space-time. In particular, we investigate lightlike submanifolds with curvature invariance, parallel second fundamental forms, totally umbilical second fundamental forms, null sectional curvatures and null Ricci curvatures, respectively.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.863-874
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• 2012

We provide a study of lightlike hypersurfaces of a generalized Robertson-Walker (GRW) space-time. In particular, we investigate lightlike hypersurfaces with curvature invariance, parallel second fundamental forms, totally umbilical second fundamental forms, null sectional curvatures and null Ricci curvatures, respectively.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.57-69
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• 2002

We study a unifying method to obtain nondegenerate isometric immersions of manifolds of constant sectional curvatures c with flat normal bundles into the space forms of curvature c for c= -1,0,1.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.665-678
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• 1997

In this paper we prove that if the minimum of the sectional curvatures of a compact n-dimensional minimal generic submanifold M of a complex projective space is 1/n, then M is the geodesic minimal hypersphere.

• The Pure and Applied Mathematics
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• v.3 no.2
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• pp.173-179
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• 1996

M be an ($n\geq3$)-dimensional compact connected and oriented Riemannian manifold isometrically immersed on an (n ＋ 2)-dimensional sphere $S^{n＋2}$(c). If all sectional curvatures of M are not less than a positive constant c, show that M is a real homology sphere.

• East Asian mathematical journal
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• v.19 no.1
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• pp.49-61
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• 2003

We study the asymptotic boundary behavior of the Bergman kernel function on the diagonal, the Bergman metric and the holomorphic sectional curvatures of the Bergman metric in bounded strongly pseudoconvex domains.

• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.143-165
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• 2023

For each connected and simply connected three-dimensional non-unimodular Lie group, we classify the left invariant Lorentzian metrics up to automorphism, and study the extent to which curvature can be altered by a change of metric. Thereby we obtain the Ricci operator, the scalar curvature, and the sectional curvatures as functions of left invariant Lorentzian metrics on each of these groups. Our study is a continuation and extension of the previous studies done in [3] for Riemannian metrics and in [1] for Lorentzian metrics on unimodular Lie groups.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.127-134
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• 2000

Let $\Omega$ be a bounded pseudoconvex domain in$C^{n}$ with smooth defining function r and let$z_0\; {\in}\; b{\Omega}$ be a point of finite type. We also assume that $\Omega$ is convex in a neighborhood of $z_0$. Then we prove that all the holomorphic sectional curvatures of the Bergman metric of $\Omega$ are bounded below by a negative constant near $z_0$.