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A VARIATIONAL PROBLEM FOR CURVES ON FINSLER SURFACES

Part of: Infinite-dimensional manifolds Existence theories

Published online by Cambridge University Press:  13 May 2016

SORIN V. SABAU  and
KAZUHIRO SHIBUYA
SORIN V. SABAU*
Affiliation:
Department of Mathematics, Tokai University, Sapporo, 005-8601, Japan email [email protected]
KAZUHIRO SHIBUYA
Affiliation:
Graduate School of Science, Hiroshima University, Hiroshima, 739-8521, Japan email [email protected]
*
✉[email protected]
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Abstract

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We study the variational problem for $N$-parallel curves on a Finsler surface by means of exterior differential systems using Griffiths’ method. We obtain the conditions when these curves are extremals of a length functional and write the explicit form of Euler–Lagrange equations for this type of variational problem.

Keywords

exterior differential systemsvariational problemsFinsler surfaces

MSC classification

Primary: 49J40: Variational methods including variational inequalities
Secondary: 58B20: Riemannian, Finsler and other geometric structures
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 101 , Issue 3 , December 2016 , pp. 418 - 430
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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