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)



Curvature estimates for complete and bounded submanifolds in a Riemannian manifold

Author: Yoshihisa Kitagawa
Journal: Proc. Amer. Math. Soc. 83 (1981), 579-581
MSC: Primary 53C20
MathSciNet review: 627696
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ M$ be a complete $ n$-dimensional submanifold in the $ (2n - 1)$-dimensional Euclidean space, with scalar curvature bounded from below. Baikousis and Koufogiorgos proved that the sectional curvature of $ M$ satisfies sup $ {K_M} \geqslant {\lambda ^{ - 2}}$ if $ M$ is contained in a ball of radius $ \lambda $. We extend this result to the case that the ambient space is a complete simply connected Riemannian manifold of nonpositive curvature.

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

  • [1] C. Baikousis and T. Koufogiorgos, Isometric immersions of complete Riemannian manifolds into Euclidean space, Proc. Amer. Math. Soc. 79 (1980), 87-88. MR 560590 (81c:53053)
  • [2] J. Cheeger and D. Ebin, Comparison theorems in Riemannian geometry, North-Holland, Amsterdam, 1975. MR 0458335 (56:16538)
  • [3] S. Kobayashi and K. Nomizu, Foundation of differential geometry, Vol. II, Interscience, New York, 1967. MR 0152974 (27:2945)
  • [4] H. Omori, Isometric immersions of Riemannian manifolds, J. Math. Soc. Japan 19 (1967), 205-214. MR 0215259 (35:6101)

Similar Articles

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

Retrieve articles in all journals with MSC: 53C20

Additional Information

Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society