No CrossRef data available.
Article contents
Complete submanifolds with parallel mean curvature in a sphere
Published online by Cambridge University Press: 18 May 2009
Extract
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.
Let Mn be an n-dimensional manifold immersed in an (n+p)-dimensional unit sphere Sn+p, with mean curvature H and second fundamental form B. We put φ(X, Y) = B(X, Y)–(X, Y)H where X and Y are tangent vector fields on Mn. Assume that the mean curvature is parallel in the normal bundle of Mn in Sn+p. Following Alencar and do Carmo [1] we denote by BH the square of the positive root of
- Type
- Research Article
- Information
- Copyright
- Copyright © Glasgow Mathematical Journal Trust 1996
References
REFERENCES
1.Alencar, H. and Carmo, M. do, Hypersurfaces with constant mean curvature in spheres, Proc. Amer. Math. Soc. 120 (1994), 1223–1229.CrossRefGoogle Scholar
2.Leung, P. F., An estimate on the Ricci curvature of a submanifold and some applications, Proc. Amer. Math. Soc. 114 (1992), 1051–1061.CrossRefGoogle Scholar
3.Xu, H. W., A rigidity theorem for submanifolds with parallel mean curvature in a sphere, Arch. Math. 61 (1993), 489–496.CrossRefGoogle Scholar
4.Yau, S. T., Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201–228.CrossRefGoogle Scholar
You have
Access