Geodesic
Connections over a~distribution and geodesic sprays
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2013), pp. 10-18.

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

We define (in a natural way) an almost contact metric structure on a smooth distribution of a contact metric manifold considered as the total space of a vector bundle. We introduce notions of a geodesic spray of a connection over a smooth distribution and of a generalized Hamiltonian system. In terms of this system we give an invariant description of the motion of a mechanical system with constraints.
Keywords: contact structure, Hamiltonian vector field, Reeb vector field, semispray, geodesic spray, symplectic structure. 
@article{IVM_2013_4_a1,
     author = {A. V. Bukusheva and S. V. Galaev},
     title = {Connections over a~distribution and geodesic sprays},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {10--18},
     publisher = {mathdoc},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_4_a1/}
}
TY  - JOUR
AU  - A. V. Bukusheva
AU  - S. V. Galaev
TI  - Connections over a~distribution and geodesic sprays
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2013
SP  - 10
EP  - 18
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2013_4_a1/
LA  - ru
ID  - IVM_2013_4_a1
ER  - 
%0 Journal Article
%A A. V. Bukusheva
%A S. V. Galaev
%T Connections over a~distribution and geodesic sprays
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2013
%P 10-18
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2013_4_a1/
%G ru
%F IVM_2013_4_a1
A. V. Bukusheva; S. V. Galaev. Connections over a~distribution and geodesic sprays. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2013), pp. 10-18. http://geodesic.mathdoc.fr/item/IVM_2013_4_a1/

[1] Vagner V. V., “Geometricheskaya interpretatsiya dvizheniya negolonomnykh dinamicheskikh sistem”, Tr. seminara po vektornomu i tenzornomu analizu, 5, 1941, 301–327 | MR | Zbl

[2] Vershik A., Faddeev L., “Differentsialnaya geometriya i lagranzheva mekhanika so svyazyami”, DAN SSSR, 202:3 (1972), 555–557 | Zbl

[3] Grifone J., “Structure presque tangente et connexions. I”, Ann. Inst. Fourier Grenoble, 22:1 (1972), 287–334 | DOI | MR | Zbl

[4] Grifone J., “Structure presque tangente et connexions. II”, Ann. Inst. Fourier Grenoble, 22:3 (1972), 291–338 | DOI | MR | Zbl

[5] Kagan F. I., “Infinitezimalnye svyaznosti v kasatelnom rassloenii i geodezicheskie pulverizatsii”, Differentsialnaya geometriya, 3, Saratov, 1977, 31–42 | MR | Zbl

[6] Szilasi J., Vincze C., “A new look at Finsler connections and special Finsler manifolds”, Acta Mathem. Academiae Paedagogicae Nyiredyhaziensis, 16 (2000), 33–63 | MR | Zbl

[7] Bucataru I., Dahl M. F., “A complete lift for semisprays”, International Journal of Geom. Methods in Modern Phys., 7:2 (2010), 267–287 | DOI | MR | Zbl

[8] Bucataru I., “Metric nonlinear connections”, Diff. Geom. and Appl., 25:3 (2007), 335—343 | DOI | MR | Zbl

[9] Pitis G., “Hamiltonian fields and energy in contact manifolds”, International J. Geom. Methods in Modern Phys., 5:1 (2008), 63–77 | DOI | MR | Zbl

[10] Eberard D. B., Maschke M., Van Der Schaft A. J., “An extension of hamiltonian systems to the thermodynamic phase space: towards a geometry of nonreversible processes”, Reports on mathematical physics, 60:2 (2000), 175–198 | DOI | MR

[11] Crasmareanu M., “Completeness of hamiltonian vector fields in Jacobi and contact geometry”, U. P. B. Sci. Bull. Ser. A, 73:2 (2011), 23–36 | MR | Zbl

[12] Galaev S. V., Gokhman A. V., “Obobschennye gamiltonovy sistemy na mnogoobraziyakh so svyaznostyu”, Matematika. Mekhanika, 2, Saratov, 2000, 16–19

[13] Vagner V. V., “Geometriya $(n-1)$-mernogo negolonomnogo mnogoobraziya v $n$-mernom prostranstve”, Tr. ceminara po vektornomu i tenzornomu analizu, 5, 1941, 173–225 | MR | Zbl

[14] Kirichenko V. F., Differentsialno-geometricheskie struktury na mnogoobraziyakh, MPGU, Moskva, 2003

[15] Galaev S. V., “Vnutrennyaya geometriya metricheskikh pochti kontaktnykh mnogoobrazii”, Izv. Sarat. un-ta. Ser. Matematika. Mekhanika. Informatika, 12:1 (2012), 16–22

[16] Galaev S. V., “Contact structures with admissible Finsler metrics”, Physical Interpretation of Relativity Theory, Proceedings of International Meeting (Moscow, 4–7 July 2011), eds. M. C. Duffy, V. O. Gladyshev, A. N. Morozov, P. Rowlands, BMSTU, Moscow, 2012, 80–87