Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



An estimate on the Ricci curvature of a submanifold and some applications

Author: Pui Fai Leung
Journal: Proc. Amer. Math. Soc. 114 (1992), 1051-1061
MSC: Primary 53C40; Secondary 53C20
MathSciNet review: 1093601
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove a best possible lower bound on the Ricci curvature of an immersed submanifold in a Euclidean space and apply it to study the size of the Gauss image of a complete noncompact hypersurface with constant positive mean curvature in a Euclidean space.

References [Enhancements On Off] (What's this?)

  • [1] S. Y. Cheng, Spectrum of the Laplacian and its applications to differential geometry, Ph.D. Dissertation, Univ. of California, Berkeley, 1974.
  • [2] M. Gage, Upper bounds for the first eigenvalue of the Laplace-Beltrami operator, Indiana Univ. Math. J. 29 (1980), 897-912. MR 589652 (82b:58095)
  • [3] D. Hoffman, R. Osserman, and R. Schoen, On the Gauss map of complete surfaces of constant mean curvature in $ {\mathbb{R}^3}$ and $ {\mathbb{R}^4}$, Comment. Math. Helv. 57 (1982), 519-531. MR 694604 (84f:53004)
  • [4] D. Laugwitz, Differential and Riemannian geometry, Academic Press, 1965. MR 0172184 (30:2406)
  • [5] P. F. Leung, Minimal submanifolds in a sphere, Math. Z. 183 (1983), 75-86. MR 701359 (85f:53052)
  • [6] B. Palmer, The Gauss map of a spacelike constant mean curvature hypersurface of Minkowski space, Comment. Math. Helv. 65 (1990), 52-57. MR 1036127 (91a:53014)

Similar Articles

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

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

Additional Information

Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society