• 대한수학회보
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• 제52권5호
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• pp.1535-1547
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• 2015

A vector field on a Riemannian manifold (M, g) is called concircular if it satisfies ${\nabla}X^v={\mu}X$ for any vector X tangent to M, where ${\nabla}$ is the Levi-Civita connection and ${\mu}$ is a non-trivial function on M. A smooth vector field ${\xi}$ on a Riemannian manifold (M, g) is said to define a Ricci soliton if it satisfies the following Ricci soliton equation: $$\frac{1}{2}L_{\xi}g+Ric={\lambda}g$$, where $L_{\xi}g$ is the Lie-derivative of the metric tensor g with respect to ${\xi}$, Ric is the Ricci tensor of (M, g) and ${\lambda}$ is a constant. A Ricci soliton (M, g, ${\xi}$, ${\lambda}$) on a Riemannian manifold (M, g) is said to have concircular potential field if its potential field is a concircular vector field. In the first part of this paper we determine Riemannian manifolds which admit a concircular vector field. In the second part we classify Ricci solitons with concircular potential field. In the last part we prove some important properties of Ricci solitons on submanifolds of a Riemannian manifold equipped with a concircular vector field.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.345-351
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• 2007

Using more precise majorizing sequences we provide a finer convergence analysis than before [1], [7] of Newton's method in Riemannian manifolds with the following advantages: weaker hypotheses, finer error bounds on the distances involved and a more precise information on the location of the singularity of the vector field.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권4호
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• pp.327-335
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• 2012

We study half lightlike submanifolds M of semi-Riemannian manifolds $\widetilde{M}$ of quasi-constant curvatures. The main result is a characterization theorem for screen homothetic Einstein half lightlike submanifolds of a Lorentzian manifold of quasi-constant curvature subject to the conditions; (1) the curvature vector field of $\widetilde{M}$ is tangent to M, and (2) the co-screen distribution is a conformal Killing one.

• 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 $\tilde{M}$.

• East Asian mathematical journal
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• 제30권1호
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• pp.15-22
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• 2014

In this paper, we study lightlike hypersurfaces M of semi-Riemannian manifolds $\bar{M}$ of quasi-constant curvatures. Our main result is a characterization theorem for screen homothetic Einstein lightlike hypersurfaces of a Lorentzian manifold of quasi-constant curvature subject such that its curvature vector field ${\zeta}$ is tangent to M.

• 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.

• 대한수학회지
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• 제32권1호
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• pp.151-160
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• 1995

The notion of finite type submanifold was introduced by B.-Y. Chen [1]. A lot of works were done in this field of study by many authors. B.-Y. Chen also extended this notion to pseudo-Riemannian submanifold of pseudo-Euclidean space ([2]).

• Korean Journal of Mathematics
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• 제23권4호
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• pp.733-740
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• 2015

In this paper, we prove the existence of warping functions on Riemannian warped product manifolds with some prescribed scalar curvatures according to the fiber manifolds of class (B).

• 대한수학회지
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• 제32권1호
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• pp.93-101
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• 1995

Let (M,g) be an n-dimensional, connected Riemannian manifold with Levi Civita connection $\nabla$ and Riemannian curvature tensor R defined by $$ R_XY = [\nabla_X, \nabla_Y] - \nabla_{[X,Y]} $$ for all smooth vector fields X, Y. $\nablaR, \cdots, \nabla^kR, \cdots$ denote the successive covariant derivatives and we assume $\nabla^0R = R$.

• 대한수학회논문집
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• 제12권2호
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• pp.325-332
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• 1997

Let $Z = X \times Y$ where X and Y are complex manifolds. We suppose that projection $\pi$ on the second factor is a Riemannian submersion, that TX is perpendicular to TY, and that the metrics on Z and on Y are Hermetian; we do not assume Z is a Riemannian product. We study when the pull-back of an eigenfunction of the complex Laplacian on Y is an eigenfunction of the complex Laplacian on Z.