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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Blaschke Finsler manifolds and actions of projective Randers changes on cut loci


Authors: Nobuhiro Innami, Yoe Itokawa, Tetsuya Nagano and Katsuhiro Shiohama
Journal: Trans. Amer. Math. Soc. 371 (2019), 7433-7450
MSC (2010): Primary 53C60, 53C20; Secondary 53C22
DOI: https://doi.org/10.1090/tran/7603
Published electronically: December 3, 2018
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Abstract: We study the cut and conjugate locus of a point in a complete Finsler manifold. Our study focuses on their intersection. We propose the Finsler version of Klingenberg's lemma and determine the structure of the cut and conjugate locus in a Blaschke Finsler manifold. In order to have some examples, we study how cut and conjugate loci change under a projective Randers change. We see the relation between invariance of cut loci and exactness of a closed $ 1$-form in its projective Randers changes.


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Additional Information

Nobuhiro Innami
Affiliation: Department of Mathematics, Faculty of Science, Niigata University, Niigata, 950-2181, JAPAN
Email: innami@math.sc.niigata-u.ac.jp

Yoe Itokawa
Affiliation: Department of Information and Communication Engineering, Fukuoka Institute of Technology, Wajiro-Higashi, Fukuoka, 811-0295 JAPAN
Email: itokawa@fit.ac.jp

Tetsuya Nagano
Affiliation: Department of Information Security, University of Nagasaki, Nagasaki, JAPAN
Email: hnagano@sun.ac.jp

Katsuhiro Shiohama
Affiliation: Fukuoka Institute of Technology, Wajiro, Higashi-ku, Fukuoka, JAPAN
Email: k-siohama@fit.ac.jp

DOI: https://doi.org/10.1090/tran/7603
Keywords: Finsler manifold, Blaschke manifold, Randers metric, cut locus, conjugate locus
Received by editor(s): October 5, 2016
Received by editor(s) in revised form: November 13, 2017, and March 30, 2018
Published electronically: December 3, 2018
Additional Notes: The research of the first and last authors was partially supported by JSPS KAKENHI Grant numbers 15K13435 and 15K04864.
Article copyright: © Copyright 2018 American Mathematical Society