• Kyungpook Mathematical Journal
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• 제57권3호
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• pp.503-516
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• 2017

In this paper, we study totally umbilical slant lightlike submanifolds of indefinite Kaehler manifolds. We prove that there do not exist totally umbilical proper slant lightlike submanifolds in indefinite Kaehler manifolds other than totally geodesic proper slant lightlike submanifolds. We also prove that there do not exist totally umbilical proper slant lightlike submanifolds of indefinite Kaehler space forms. Finally, we give a characterization theorem on minimal slant lightlike submanifolds.

• Kyungpook Mathematical Journal
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• 제48권2호
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• pp.183-194
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• 2008

We prove that totally umbilical submanifold M of an extended quasi-recurren manifold is also extended quasi-recurrent. If, moreover, M is conformally flat then, locally, M is isometric to the manifold with known metric. Some curvature properties of such submanifold are investigated. Making use of these results we shall prove the existence of totally umbilical submanifold being pseudosymmetric in the sense of Ryszard Deszcz and satisfying some other curvature conditions.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권1호
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• pp.51-63
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• 2010

In this paper, we prove two characterization theorems for real half lightlike submanifold (M,g,S(TM)) of an indefinite Kaehler manifold $\bar{M}$ or an indefinite complex space form $\bar{M}$(c) subject to the conditions : (a) M is totally umbilical in $\bar{M}$, or (b) its screen distribution S(TM) is totally umbilical in M.

• 충청수학회지
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• 제22권3호
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• pp.409-416
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• 2009

In this paper, we study the geometry of lightlike hypersurfaces of a semi-Riemannian manifold. We prove a classification theorem for lightlike hypersurfaces M with totally umbilical screen distributions of a semi-Riemannian space form.

• 대한수학회논문집
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• 제25권3호
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• pp.443-450
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• 2010

In this paper, we study the geometry of lightlike real hyper-surfaces of an indefinite Kaehler manifold. The main result is a characterization theorem for lightlike real hypersurfaces M of an indefinite complex space form $\bar{M}(c)$ such that the screen distribution is totally umbilic.

• 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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• 제17권1호
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• pp.29-38
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• 2010

We study the geometry of half light like submanifold M of a semi-Riemannian space form $\bar{M}$(c) subject to the conditions : (a) the screen distribution on M is totally umbilic in M and the coscreen distribution on M is conformal Killing on $\bar{M}$ or (b) the screen distribution is totally geodesic in M and M is irrotational.

• 대한수학회보
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• 제54권6호
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• pp.2001-2011
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• 2017

In 1997, H. Li [12] proposed a conjecture: if $M^n(n{\geqslant}3)$ is a complete spacelike hypersurface in de Sitter space $S^{n+1}_1(1)$ with constant normalized scalar curvature R satisfying $\frac{n-2}{n}{\leqslant}R{\leqslant}1$, then is $M^n$ totally umbilical? Recently, F. E. C. Camargo et al. ([5]) partially proved the conjecture. In this paper, from a different viewpoint, we study closed convex spacelike hypersurface $M^n$ in locally symmetric Lorentz space $L^{n+1}_1$ and also prove that $M^n$ is totally umbilical if the square of length of second fundamental form of the closed convex spacelike hypersurface $M^n$ is constant, i.e., Theorem 1. On the other hand, we obtain that if the sectional curvature of the closed convex spacelike hypersurface $M^n$ in locally symmetric Lorentz space $L^{n+1}_1$ satisfies $K(M^n)$ > 0, then $M^n$ is totally umbilical, i.e., Theorem 2.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제8권1호
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• pp.33-46
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• 2001

The purpose of this paper is to study totally umbilical coisotropic sub-manifold(M. g, SM) of a semi-Riemannian manifold(M,g)

• 대한수학회논문집
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• 제29권2호
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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.