Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-05T11:13:05.242Z Has data issue: false hasContentIssue false
  • English
  • Français

Indefinite rigidity of complex submanifolds and maximal surfaces

Published online by Cambridge University Press:  24 October 2008

Kinetsu Abe  and
Martin A. Magid
Kinetsu Abe
Affiliation:
Department of Mathematics, University of Connecticut, Storrs, Connecticut 06268, U.S.A.
Martin A. Magid
Affiliation:
Department of Mathematics, Wellesley College, Wellesley, Massachusetts 02181, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Extract

In 1953, Calabi proved a rigidity theorem for Kählerian submanifolds in complex space forms [3]. The Calabi rigidity theorem, since then, has been successfully applied to various areas in geometry. Among them is the study of minimal surfaces in real space forms; see [4] for example.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 3 , November 1989 , pp. 481 - 494
Copyright
Copyright © Cambridge Philosophical Society 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Abe, K. and Magid, M.. Complex analytic curves and maximal surfaces. (Submitted.)Google Scholar
[2]Abe, K. and Magid, M.. Rigidity of submanifolds in indefinite Kählerian space forms. (Submitted.)Google Scholar
[3]Calabi, E.. Isometric embeddings of complex manifolds. Ann. of Math. 58 (1953), 1–23.CrossRefGoogle Scholar
[4]Lawson, H. B. Jr. Lectures on Minimal Submanifolds. vol. 1 (Publish or Perish, Inc., 1980).Google Scholar
[5]O'Neill, B.. Semi-Riemannian Geometry with Applications to Relativity (Academic Press, 1983).Google Scholar