Blaschke Finsler manifolds and actions of projective Randers changes on cut loci
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- by Nobuhiro Innami, Yoe Itokawa, Tetsuya Nagano and Katsuhiro Shiohama PDF
- Trans. Amer. Math. Soc. 371 (2019), 7433-7450 Request permission
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.References
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Additional Information
- Nobuhiro Innami
- Affiliation: Department of Mathematics, Faculty of Science, Niigata University, Niigata, 950-2181, JAPAN
- MR Author ID: 199776
- 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
- MR Author ID: 261071
- Email: itokawa@fit.ac.jp
- Tetsuya Nagano
- Affiliation: Department of Information Security, University of Nagasaki, Nagasaki, JAPAN
- MR Author ID: 254796
- Email: hnagano@sun.ac.jp
- Katsuhiro Shiohama
- Affiliation: Fukuoka Institute of Technology, Wajiro, Higashi-ku, Fukuoka, JAPAN
- MR Author ID: 160870
- Email: k-siohama@fit.ac.jp
- 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.
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 7433-7450
- MSC (2010): Primary 53C60, 53C20; Secondary 53C22
- DOI: https://doi.org/10.1090/tran/7603
- MathSciNet review: 3939582