• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.135-146
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• 2001

Let M(sup)n be a space-ike submanifold in a de Sitter space M(sub)p(sup)n+p (c) with constant scalar curvature. We firstly extend Cheng-Yau's Technique to higher codimensional cases. Then we study the rigidity problem for M(sup)n with parallel normalized mean curvature vector field.

• East Asian mathematical journal
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• v.16 no.1
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• pp.135-145
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• 2000

The purpose of this paper is to study the Chern-type problem of the complete space-like submanifolds of an indefinite complex space form.

• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.109-121
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• 2008

We determine maximal space-like hypersurfaces which are the images of subbundles of the normal bundle of m-dimensional totally geodesic space-like submanifolds of an (m + 2)-dimensional Lorentzian space form $\tilde{M}_1^{m+2}$(c) under the normal exponential map. Then we construct examples of maximal space-like hypersurfaces of $\tilde{M}_1^{m+2}$(c).

• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1145-1168
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• 1999

The purpose of this paper is to study the complete submanifolds with restricted space-like and time-like holomorphic bisectional curvatures in an indefinite locally symmetric K hler manifold.

• Bulletin of the Korean Mathematical Society
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• v.26 no.1
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• pp.75-82
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• 1989

It is recently proved by Aiyama and the authors [2] that a complete space-like complex submanifold of a complex space form $M^{n+p}$$_{p}$ (c') (c'.geq.0) is to totally geodesic. This is a complex version of the Bernstein-type theorem in the Minkowski space due to Calabi [4] and Cheng and Yau [5], which is generalized by Nishikawa[7] in the Lorentz manifold satisfying the strong energy condition. The purpose of this paper is to consider his result in the complex Lorentz manifold and is to prove the following.e following.

• The Pure and Applied Mathematics
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• v.17 no.1
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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.