Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지

SPACE-LIKE SUBMANIFOLDS WITH CONSTANT SCALAR CURVATURE IN THE DE SITTER SPACES

  • Liu, Ximin (Department of Applied Mathematics, Dalian University of Technology)
  • Published : 2001.01.01
Download PDF
⟨ Previous Next ⟩

Abstract

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.

Keywords

References

  1. Tokyo J.Math. v.18 Compact space-like submanifolds in a pseudo-Riemannian sphere Sm+p(c) R.Aiyama
  2. Proc.Amer.Math.Soc. v.120 Hypersurfaces with constant mean curvature in spheres H.Alencar;M.P.do Carmo
  3. Math.Z. v.196 On space-like hypersurfaces with constant mean curvature in the de Sitter space K.Akutagawa
  4. Math.Z. v.206 Complete space-like submanifolds in a de Sitter space with parallel mean curvature vector Q.M.Cheng
  5. Math.Ann. v.225 Hypersurfaces with constant scalar curvature S.Y.Cheng;S.T.Yau
  6. Proc.amer.Math.Soc. v.125 Hypersurfaces in sphere with constant mean curvature Z.H.Hou
  7. Math.Ann. v.305 Hypersurfaces with constant scalar curvature in space forms H.Li
  8. Ark.Mat. v.35 Global rigidity theorems of Hypersurfaces
  9. Semi-Riemannian Geometry B.O'Neill
  10. Amer.J.Math. v.96 Hypersurfaces and a pinching problem on the second fundamental tensor M.Okumuru
  11. Indiana Univ.Math.J. v.36 Complete space-like hypersurfaces of constant mean curvature in the de Sitter space J.Ramanathan
  12. Tohoku Math.J. v.46 Submanifolds with parallel mean curvature vector in spheres W.Santos
  13. J.Diff.Geom. v.6 Submanifolds with parallel mean curvature vector K.Yano;S.Ishihara
  14. Amer.J.Math. v.96 Submanifolds with constant mean curvature S.T.Yau
  15. Amer.J.Math. v.97 Submanifolds with constant mean curvature S.T.Yau
  16. Diff.Goem.and its Appl. v.6 Space-like hypersurfaces with constant scalar curvature in the de Sitter spaces Y.Zheng