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On some types of geodesics on Riemannian manifolds

Published online by Cambridge University Press:  22 January 2016

Tetsunori Kurogi
Tetsunori Kurogi*
Affiliation:
Fukui University
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For a given Riemannian manifold M and its submanifold N, one can find various types of geodesies on M starting from any point of N and ending in any point of N. For example, geodesies which start perpendicularly from N and end perpendicularly in N are treated by many mathematicians. K. Grove has stated a condition in a general case for the existence of such a geodesic ([4]), where he has used the method of the infinite dimensional critical point theory. This method is very useful for the study of geodesies and many geometricians have used it successfully. It has two aspects: one is an existence theory and the other is a quantitative theory, which one can find, for instance, in the excellent theory for closed geodesies of W. Klingenberg ([1], [7]) and so on.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 81 , March 1981 , pp. 27 - 43
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1981

References

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