Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-05T01:42:03.187Z Has data issue: false hasContentIssue false

RIGIDITY THEOREMS FOR HYPERSURFACES WITH CONSTANT SCALAR CURVATURE IN A UNIT SPHERE

Published online by Cambridge University Press:  09 August 2007

GUOXIN WEI
Affiliation:
Department of Mathematics, Kyungpook National University 702-701, Taegu Republic of Korea e-mail: [email protected]
YOUNG JIN SUH
Affiliation:
Department of Mathematics, Kyungpook National University 702-701, Taegu Republic of Korea e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we give a characterization of Clifford tori and in a unit sphere S n+1 (1). Our results extend the results due to Cheng and Yau [4], and Wang and Xia [11].

Keywords

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2007

References

REFERENCES

1. Luis, J. Alias, de Almeida, Sebastião C. and Brasil, Aldir Jr., Hypersurfaces with constant mean curvature and two principal curvatures in S n+1 , An. Acad. Brasil. Cienc. 76 (2004), 489497.Google Scholar
2. Cartan, E., Familles de surfaces isoparametriques dans les espaces a courvure constante, Ann. of Math. 17 (1938), 177191.Google Scholar
3. Cheng, Q. M., Hypersurfaces in a unit sphere S n+1 (1) with constant scalar curvature, J. London Math. Soc. (2) 64 (2002), 755768.CrossRefGoogle Scholar
4. Cheng, S. Y. and Yau, S. T., Hypersurfaces with constant scalar curvature, Math. Ann. 225 (1977), 195204.Google Scholar
5. Chern, S. S., Carmo, M. do and Kobayashi, S., Minimal submanifolds of a sphere with second fundamental form of constant length, Functional analysis and related fields (Proc. Conf. for M. Stone, Univ. of Chicago, Chicago 1968), (Spinger-Verlag, 1970), 5975.Google Scholar
6. Lawson, H. B., Local rigidity theorems for minimal hypersurfaces, Ann. of Math. 89 (1969), 179185.CrossRefGoogle Scholar
7. Li, H., Hypersurfaces with constant scalar curvature in space forms, Math. Ann. 305 (1996), 665672.Google Scholar
8. Li, H., Global rigidity theorems of hypersurface, Ark. Mat. 35 (1997), 327351.CrossRefGoogle Scholar
9. Otsuki, T., Minimal hypersurfaces in a Riemannian manifold of constant curvature, Amer. J. Math. 92 (1970), 145173.CrossRefGoogle Scholar
10. Suh, Y. J. and Yang, H. Y., Kaehler submanifolds with Ricci curvature bounded from below, Michigan Math. J. 53 (2005), 545552.CrossRefGoogle Scholar
11. Wang, Q. L. and Xia, C. Y., Rigidity theorems for closed hypersurfaces in space forms, Quart. J. Math. Oxford Ser. (2) 56 (2005), 101110.Google Scholar
12. Wei, G., Complete hypersurfaces with constant mean curvature in a unit sphere, Monatsh. Math. 149 (2006), 251258.Google Scholar
13. Wei, G., Rigidity theorems for hypersurfaces in a unit sphere, Monatsh. Math. 149 (2006), 343350.CrossRefGoogle Scholar