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

MathSciNet review:
1260187

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We classify the complete and non-negatively curved hypersurfaces of constant mean curvature in spaces of constant sectional curvature.

**[1]**S. I. Goldberg,*An application of Yau’s maximum principle to conformally flat spaces*, Proc. Amer. Math. Soc.**79**(1980), no. 2, 268–270. MR**565352**, 10.1090/S0002-9939-1980-0565352-8**[2]**Thomas Hasanis,*Characterization of totally umbilical hypersurfaces*, Proc. Amer. Math. Soc.**81**(1981), no. 3, 447–450. MR**597660**, 10.1090/S0002-9939-1981-0597660-X**[3]**Katsumi Nomizu and Brian Smyth,*A formula of Simons’ type and hypersurfaces with constant mean curvature*, J. Differential Geometry**3**(1969), 367–377. MR**0266109****[4]**Masafumi Okumura,*Hypersurfaces and a pinching problem on the second fundamental tensor*, Amer. J. Math.**96**(1974), 207–213. MR**0353216****[5]**Hideki Omori,*Isometric immersions of Riemannian manifolds*, J. Math. Soc. Japan**19**(1967), 205–214. MR**0215259****[6]**Brian Smyth,*Submanifolds of constant mean curvature*, Math. Ann.**205**(1973), 265–280. MR**0334102****[7]**S. T. Yau,*Submanifolds with constant mean curvature*, Amer. J. Math.**97**(1975), 76-100.**[8]**Shing Tung Yau,*Harmonic functions on complete Riemannian manifolds*, Comm. Pure Appl. Math.**28**(1975), 201–228. MR**0431040**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
53C40,
53C20

Retrieve articles in all journals with MSC: 53C40, 53C20

Additional Information

DOI:
http://dx.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