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A sharp lower bound for the Ricci curvature of bounded hypersurfaces in space forms

Published online by Cambridge University Press:  17 April 2009

Alain R. Veeravalli
Affiliation:
Département de Mathématiques, Université d'Evry-Val d'Essonne, Boulevard des Coquibus, 91025 Evry Cedex, France e-mail: [email protected]
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Abstract

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Dedicated to Lamiae and Lucas Zakaria with great affection.

We give a sharp lower bound for the Ricci curvature of bounded complete hypersurfaces of space forms. This leads to several applications.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Beltagy, M., ‘A study of Ricci curvature of space forms’, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 126 (1992), 177185.Google Scholar
[2]Cheeger, J. and Ebin, D.G., Comparison theorems in Riemannian geometry (North-Holland, Amsterdam, 1975).Google Scholar
[3]Erdŏgan, M., ‘On the Ricci curvature of a hypersurface in a space form’, Geom. Dedicata 61 (1996), 221225.CrossRefGoogle Scholar
[4]Leung, P.F., ‘Complete hypersurface of non-positive Ricci curvature’, Bull. Austral. Math. Soc. 27 (1983), 215219.CrossRefGoogle Scholar
[5]Omori, H., ‘Isometric immersions of Riemannian manifolds’, J. Math. Soc. Japan 19 (1967), 205214.Google Scholar
[6]Sakai, T., Riemannian geometry, Translations of Mathematical Monographs 149 (Amer. Math. Soc., Providence, R.I., 1996).CrossRefGoogle Scholar
[7]Spivak, M., A comprehensive introduction to differential geometry 5 (Publish or Perish, Boston, Mass., 1975).Google Scholar
[8]Veeravalli, A.R., ‘A rigidity theorem for compact hypersurfaces with an upper bound for the Ricci curvature’, Geometriae Dedicata 74 (1999), 287290.CrossRefGoogle Scholar