Abstract
We introduce a class of submersions between two Finslerian manifolds and the class of Finsler-compatible maps which contains the previous class. Defining also the notion of stretch it follows an upper bound for the stretch of these submersions. If the support manifold for the considered Finslerian geometries is the same we introduce a new function, called conformality, as a way to measure quantitatively the difference between the given geometries.
Keywords
Finsler fundamental function Finsler metric submersion Finsler-compatible map stretch conformality
References
- Álvarez Paiva, J. C. and Durán, C. E., Isometric submersions of Finsler manifolds, Proc. Am. Math. Soc. 129(8), (2001), 2409--2417.
- Anastasiei M., Certain generalizations of Finsler metrics, in Bao, David (Ed.) et al., Finsler geometry. Joint summer research conference, July 16-20, 1995, Seattle, WA, USA. Providence, RI: American Mathematical Society. Contemp. Math. 196, 161--169, 1996.
- Crasmareanu M., Fibre bundle maps and complete sprays in Finslerian setting, J. Korean Math. Soc. 46(3), (2009), 551--560.
- Crasmareanu M., New tools in Finsler geometry: stretch and Ricci solitons, Math. Rep. (Bucur.) 16(66)(1), (2014), 83--93.
- Hsu, Agnes Chi-Ling, A characterization of the Hopf map by stretch, Math. Z. 129, (1972), 195--206.
- Ou, Ye-Lin and Wilhelm, F., Horizontally homothetic submersions and nonnegative curvature, Indiana Univ. Math. J. 56(1), (2007), 243--261.
- Popescu, P., and Popescu, M., Lagrangians adapted to submersions and foliations, Differ. Geom. Appl. 27(2), (2009), 171--178.
- Şahin, B., Riemannian submersions, Riemannian maps in Hermitian geometry, and their applications, Amsterdam: Elsevier/Academic Press, 2017.
- Wolf, J. A., Differentiable fibre spaces and mappings compatible with Riemannian metrics, Mich. Math. J. 11, (1964), 65--70.
Abstract
References
- Álvarez Paiva, J. C. and Durán, C. E., Isometric submersions of Finsler manifolds, Proc. Am. Math. Soc. 129(8), (2001), 2409--2417.
- Anastasiei M., Certain generalizations of Finsler metrics, in Bao, David (Ed.) et al., Finsler geometry. Joint summer research conference, July 16-20, 1995, Seattle, WA, USA. Providence, RI: American Mathematical Society. Contemp. Math. 196, 161--169, 1996.
- Crasmareanu M., Fibre bundle maps and complete sprays in Finslerian setting, J. Korean Math. Soc. 46(3), (2009), 551--560.
- Crasmareanu M., New tools in Finsler geometry: stretch and Ricci solitons, Math. Rep. (Bucur.) 16(66)(1), (2014), 83--93.
- Hsu, Agnes Chi-Ling, A characterization of the Hopf map by stretch, Math. Z. 129, (1972), 195--206.
- Ou, Ye-Lin and Wilhelm, F., Horizontally homothetic submersions and nonnegative curvature, Indiana Univ. Math. J. 56(1), (2007), 243--261.
- Popescu, P., and Popescu, M., Lagrangians adapted to submersions and foliations, Differ. Geom. Appl. 27(2), (2009), 171--178.
- Şahin, B., Riemannian submersions, Riemannian maps in Hermitian geometry, and their applications, Amsterdam: Elsevier/Academic Press, 2017.
- Wolf, J. A., Differentiable fibre spaces and mappings compatible with Riemannian metrics, Mich. Math. J. 11, (1964), 65--70.
Details
| Primary Language | English |
|---|---|
| Journal Section | Review Articles |
| Authors | |
| Publication Date | February 1, 2019 |
| Submission Date | November 19, 2017 |
| Acceptance Date | April 27, 2018 |
| Published in Issue | Year 2019 Volume: 68 Issue: 1 |
Cite
Cited By
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