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Tangent vectors to sets in the theory of geodesics

Published online by Cambridge University Press:  22 January 2016

Dumitru Motreanu
Dumitru Motreanu*
Affiliation:
Department of Mathematics, University of Iaşi, 6600 Iaşi, Romania
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In the setting of Banach manifolds the notion of tangent vector to an arbitrary closed subset has been introduced in [11] by the author and N. H. Pavel, and it has been used in flow-invariance and optimization ([11], [12], [13]). For detailed informations on tangent vectors to closed sets (including historical comments) we refer to the recent book of N. H. Pavel [17].

The aim of this paper is to apply this general concept of tangency in the study of geodesies. We are concerned with geodesies which have either the endpoints in given closed subsets or the same angle for a fixed closed subset. This approach allows one to extend important results due to K. Grove [4] and T. Kurogi ([6], [7]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 106 , June 1987 , pp. 29 - 47
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

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