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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.
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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

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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