Geodesic
Maximally movable spaces of Finsler type and their generalization
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 1, pp. 109-119 
V. I. Panzhensky; O. V. Sukhova. Maximally movable spaces of Finsler type and their generalization. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 1, pp. 109-119. http://geodesic.mathdoc.fr/item/FPM_2010_16_1_a8/
@article{FPM_2010_16_1_a8,
     author = {V. I. Panzhensky and O. V. Sukhova},
     title = {Maximally movable spaces of {Finsler} type and their generalization},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {109--119},
     year = {2010},
     volume = {16},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2010_16_1_a8/}
}
TY  - JOUR
AU  - V. I. Panzhensky
AU  - O. V. Sukhova
TI  - Maximally movable spaces of Finsler type and their generalization
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2010
SP  - 109
EP  - 119
VL  - 16
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/FPM_2010_16_1_a8/
LA  - ru
ID  - FPM_2010_16_1_a8
ER  - 
%0 Journal Article
%A V. I. Panzhensky
%A O. V. Sukhova
%T Maximally movable spaces of Finsler type and their generalization
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2010
%P 109-119
%V 16
%N 1
%U http://geodesic.mathdoc.fr/item/FPM_2010_16_1_a8/
%G ru
%F FPM_2010_16_1_a8

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we consider some generalization of maximally movable spaces of Finsler type. Among them, there are locally conic spaces (Riemannian metrics of their tangent spaces are realized on circular cones) and generalized Lagrange spaces with Tamm metrics (their tangent Riemannian spaces admit all rotations). On the tangent bundle of a Riemannian manifold, we study a special class of almost product metrics, generated Tamm metric. This class contains Sasaki metric and Cheeger–Gromol metric. We determine the position of this class in the Naveira classification of Riemannian almost product metrics.

[1] Panzhenskii V. I., O gruppakh izometrii metricheskikh prostranstv lineinykh elementov., Dep. v VINITI 29.04.81, No 1939-81 | MR

[2] Panzhenskii V. I., “O prostranstve lineinykh elementov nepotentsialnoi metriki s gruppoi izometrii maksimalnoi razmernosti”, Voprosy differentsialnoi geometrii v tselom, Mezhvuz. sb. nauch. trudov, LGPI, L., 1983, 91–95 | MR

[3] Panzhenskii V. I., Nekotorye voprosy geometrii metricheskikh prostranstv lineinykh elementov, Dep. v VINITI 11.12.1984, No 8179-84

[4] Panzhenskii V. I., Sukhova O. V., “K geometrii prostranstv s metrikoi Tamma”, Laptevskie chteniya, Sb. trudov Mezhdunar. geom. semin. im. G. F. Lapteva (26–31 yanvarya 2004 g.), PGPU, Penza, 2004, 93–99

[5] Rund Kh., Differentsialnaya geometriya finslerovykh prostranstv, Nauka, M., 1981 | MR | Zbl

[6] Gil-Medrano O., “Geometric properties of some classes of Riemannian almost-product manifolds”, Rend. Circ. Mat. Palermo, 32:3 (1983), 315–329 | DOI | MR | Zbl

[7] Matsumoto M., Foundation of Finsler geometry and Special Finsler Spaces, Kaiseisha Press, 1986 | MR | Zbl

[8] Moor A., “Entwicklung einer Geometrie der allgemeiner metrischen Linienelement raume”, Acta Sci. Math., 17:1–2 (1956), 85–120 | MR | Zbl

[9] Naveira A. M., “A classification of Riemannian almost-product manifolds”, Rend. Mat. Appl., 3:3 (1983), 577–592 | MR | Zbl

[10] Wang H. S., “On Finsler spaces with completely integrable equations of Killing”, J. London Math. Soc., 22 (1947), 5–9 | DOI | MR | Zbl