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Complete hypersurfaces with constant mean curvature and nonnegative sectional curvatures


Author: Ze Jun Hu
Journal: Proc. Amer. Math. Soc. 123 (1995), 2835-2840
MSC: Primary 53C40; Secondary 53C20
DOI: https://doi.org/10.1090/S0002-9939-1995-1260187-6
MathSciNet review: 1260187
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Abstract: We classify the complete and non-negatively curved hypersurfaces of constant mean curvature in spaces of constant sectional curvature.


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  • [1] S. I. Goldberg, An application of Yau's maximum principle to conformally flat spaces, Proc. Amer. Math. Soc. 79 (1980), 268-270. MR 565352 (81j:53043)
  • [2] T. Hasanis, Characterization of totally umbilical hypersurfaces, Proc. Amer. Math. Soc. 81 (1981), 447-450. MR 597660 (82e:53079)
  • [3] K. Nomizu and B. Smyth, A formula of Simons' type and hypersurfaces with constant mean curvature, J. Differential Geom. 3 (1969), 367-377. MR 0266109 (42:1018)
  • [4] M. Okumura, Hypersurfaces and a pinching problem on the second fundamental tensor, Amer. J. Math. 96 (1974), 207-213. MR 0353216 (50:5701)
  • [5] H. Omori, Isometric immersions of Riemannian manifolds, J. Math. Soc. Japan 19 (1967), 205-214. MR 0215259 (35:6101)
  • [6] B. Smyth, Submanifolds of constant mean curvature, Math. Ann. 205 (1973), 265-280. MR 0334102 (48:12421)
  • [7] S. T. Yau, Submanifolds with constant mean curvature, Amer. J. Math. 97 (1975), 76-100.
  • [8] -, Harmonic functions on complete Riemannian manifolds, Comm. Pure. Appl. Math. 28 (1975), 201-208. MR 0431040 (55:4042)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1260187-6
Keywords: Hypersurfaces of constant mean curvature, sectional curvature, totally umbilical
Article copyright: © Copyright 1995 American Mathematical Society

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