Öz
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.
Anahtar Kelimeler
Finsler fundamental function Finsler metric submersion Finsler-compatible map stretch conformality
Kaynakça
- 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.
Öz
Kaynakça
- 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.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Şubat 2019 |
| Gönderilme Tarihi | 19 Kasım 2017 |
| Kabul Tarihi | 27 Nisan 2018 |
| Yayımlandığı Sayı | Yıl 2019 Cilt: 68 Sayı: 1 |
Kaynak Göster
Cited By
The fundamental equations of a pseudo-Finsler submersion
Annali di Matematica Pura ed Applicata (1923 -)
https://doi.org/10.1007/s10231-023-01305-2
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
