A note on the existence of tubular neighbourhoods on Finsler manifolds and minimization of orthogonal geodesics to a submanifold
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- by Benigno Alves and Miguel Angel Javaloyes PDF
- Proc. Amer. Math. Soc. 147 (2019), 369-376 Request permission
Abstract:
In this note, we prove that given a submanifold $P$ in a Finsler manifold $(M,F)$, (i) the orthogonal geodesics to $P$ minimize the distance from $P$ at least in some interval, (ii) there exist tubular neighbourhoods around each point of $P$, (iii) the distance from $P$ is smooth in some open neighbourhood of $P$ (but not necessarily in $P$).References
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Additional Information
- Benigno Alves
- Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010,05508 090 São Paulo, Brazil
- Email: gguialves@hotmail.com, benigno@ime.usp.br
- Miguel Angel Javaloyes
- Affiliation: Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Espinardo, Murcia, Spain
- MR Author ID: 701910
- Email: majava@um.es
- Received by editor(s): February 10, 2018
- Received by editor(s) in revised form: May 5, 2018
- Published electronically: October 18, 2018
- Additional Notes: The first author was supported by CNPq (PhD fellowship) and partially supported by PDSE-Capes (PhD sandwich program).
This work is a result of the activity developed within the framework of the Programme in Support of Excellence Groups of the Región de Murcia, Spain, by Fundación Séneca, Science and Technology Agency of the Región de Murcia. The second author was partially supported by Spanish MINECO/FEDER project reference MTM2015-65430-P and Fundación Séneca (Región de Murcia) project 19901/GERM/15. - Communicated by: Jia-Ping Wang
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 369-376
- MSC (2010): Primary 53B40
- DOI: https://doi.org/10.1090/proc/14229
- MathSciNet review: 3876756