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Umbilical Submanifolds and Morse Functions

Published online by Cambridge University Press:  22 January 2016

Katsumi Nomizu  and
Lucio Rodríguez
Katsumi Nomizu
Affiliation:
Brown University
Lucio Rodríguez
Affiliation:
Brown University
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Let Mn be a differentiable manifold (of class C∞). By a Morse function on Mn we mean a differentiable function whose critical points are all non-degenerate. If f is an immersion of Mn into a Euclidean space Rm, we may obtain Morse functions on Mn in the following way.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 48 , December 1972 , pp. 197 - 201
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1972

References

[1] Cartan, Ē., Leçons sur la géométrie des espaces de Riemann, deuxième édition, Gauthier-Villars, Paris, 1946.Google Scholar
[2] Milnor, J., Morse Theory, Ann. of Math. Studies, No. 51, Princeton University Press, 1963.Google Scholar