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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

On geodesics of Finsler metrics via navigation problem


Authors: Libing Huang and Xiaohuan Mo
Journal: Proc. Amer. Math. Soc. 139 (2011), 3015-3024
MSC (2010): Primary 58B20
Published electronically: January 13, 2011
MathSciNet review: 2801641
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Abstract: This paper is devoted to a study of geodesics of Finsler metrics via Zermelo navigation. We give a geometric description of the geodesics of the Finsler metric produced from any Finsler metric and any homothetic field in terms of navigation representation, generalizing a result previously only known in the case of Randers metrics with constant $ S$-curvature. As its application, we present explicitly the geodesics of the Funk metric on a strongly convex domain.


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Additional Information

Libing Huang
Affiliation: School of Mathematical Sciences, Nankai University, Tianjin 300071, People’s Republic of China
Email: huanglb@nankai.edu.cn

Xiaohuan Mo
Affiliation: Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
Email: moxh@pku.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10726-3
Received by editor(s): June 30, 2010
Received by editor(s) in revised form: August 3, 2010
Published electronically: January 13, 2011
Additional Notes: This work is supported by the National Natural Science Foundation of China 11071005
The second author is the corresponding author
Communicated by: Jianguo Cao
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.