Hostname: page-component-84b7d79bbc-g78kv Total loading time: 0 Render date: 2024-07-29T21:11:07.018Z Has data issue: false hasContentIssue false
  • English
  • Français

On the codimension of a minimal immersion

Published online by Cambridge University Press:  17 April 2009

Pui-Fai Leung
Pui-Fai Leung
Affiliation:
Department of Mathematics, National University of Singapore, Singapore 0511.
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.

We show that a certain local pinching condition on a compact minimal submanifold in a sphere leads to a condition on the codimension of the immersion.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 30 , Issue 3 , December 1984 , pp. 431 - 433
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Eells, J. and Lemaire, L., “A report on harmonic maps”, Bull. London Math. Soc. 10(1978), 1–68.CrossRefGoogle Scholar
[2]Moore, J.D., “Isometric immersions of space forms in space forms”, Pacific J. Math. 40(1972), 157–166.CrossRefGoogle Scholar
[3]Ruh, E.A., “Riemannian manifolds with bounded curvature ratios”, J. Diff. Geom. 17(1982), 643–653.Google Scholar
[4]Spivak, M., A comprehensive introduction to differential geometry, (Volume 5, Publish or Perish 1975).Google Scholar
[5]Yau, S.T., “Submanifolds with constant mean curvature II”, Amer. J. Math. 97(1975), 76–100.CrossRefGoogle Scholar