Geodesic
Almost contact metric structures defined by connection over distribution with admissible Finslerian metric
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 3, pp. 17-22 
A. V. Bukusheva; S. V. Galaev. Almost contact metric structures defined by connection over distribution with admissible Finslerian metric. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 3, pp. 17-22. http://geodesic.mathdoc.fr/item/ISU_2012_12_3_a2/
@article{ISU_2012_12_3_a2,
     author = {A. V. Bukusheva and S. V. Galaev},
     title = {Almost contact metric structures defined by connection over distribution with admissible {Finslerian} metric},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {17--22},
     year = {2012},
     volume = {12},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2012_12_3_a2/}
}
TY  - JOUR
AU  - A. V. Bukusheva
AU  - S. V. Galaev
TI  - Almost contact metric structures defined by connection over distribution with admissible Finslerian metric
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2012
SP  - 17
EP  - 22
VL  - 12
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ISU_2012_12_3_a2/
LA  - ru
ID  - ISU_2012_12_3_a2
ER  - 
%0 Journal Article
%A A. V. Bukusheva
%A S. V. Galaev
%T Almost contact metric structures defined by connection over distribution with admissible Finslerian metric
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2012
%P 17-22
%V 12
%N 3
%U http://geodesic.mathdoc.fr/item/ISU_2012_12_3_a2/
%G ru
%F ISU_2012_12_3_a2

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

The notion of the intrinsic connection and the extended connection of an almost contact metric manifold $D$ with admissible Finslerian metric is introduced and studied. Using this and the extended connection on $D$ as on the total space of a vector bundle, an almost contact metric structure is defined and investigated.

[1] Bukusheva A. V., Galaev S. V., Ivanchenko I. P., “O pochti kontaktnykh metricheskikh strukturakh, opredelyaemykh svyaznostyu nad raspredeleniem s finslerovoi metrikoi”, Matematika. Mekhanika: sb. nauch. tr., 13, Izd-vo Sarat. un-ta, Saratov, 2011, 10–14 | MR

[2] Galaev S. V., “O prodolzhenii vnutrennei svyaznosti negolonomnogo mnogoobraziya s finslerovoi metrikoi”, Matematika. Mekhanika: sb. nauch. tr., 13, Izd-vo Sarat. un-ta, Saratov, 2011, 25–28

[3] Miron R., “Techniques of Finsler geometry in the theory of vector bundles”, Acta Sci. Math., 49 (1985), 119–129 | MR | Zbl

[4] Sai Prasad K., “Quarter symmetric metric Finsler connections on Kenmotsu and P-Kenmotsu vector bundles”, Intern. Math. Forum, 3:18 (2008), 847–855 | MR | Zbl

[5] Galaev S. V., “Contact structures with admissible Finsler metrics”, Physical Interpretation of Relativity Theory, Proceedings of Intern. Meeting (Moscow, 4–7 July 2011), BMSTU, Moscow, 2012, 80–87

[6] Chern S. S., “Pseudogroupes continus infinis”, Colloques Internat. Centre Nat. Rech. Sci., 52 (1953), 119–136 | MR | Zbl

[7] Gray J. W., “Some global properties of contact structures”, Ann. of Math., 69:2 (1959), 421–450 | DOI | MR | Zbl

[8] Sasaki S., “On differentiable manifolds with certain structures which are closely related to almost contact structure”, Tôhoku Math. J. Second Series, 12:3 (1960), 459–476 | DOI | MR | Zbl

[9] Blair D. E., Contact manifolds in Riemannian geometry, Springer-Verlag, Berlin–N.Y., 1976, 146 pp. | MR | Zbl

[10] Kirichenko V. F., “Metody obobschennoi ermitovoi geometrii v teorii pochti kontaktnykh mnogoobrazii”, Itogi nauki i tekhniki. Ser. Probl. geom., 18, VINITI, 1986, 25–71 | MR | Zbl

[11] Kirichenko V. F., Rustanov A. R., “Differentsialnaya geometriya kvazi-sasakievykh mnogoobrazii”, Mat. sb., 193:8 (2002), 71–100 | DOI | MR | Zbl

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

[13] Vagner V. V., Differentsialnaya geometriya negolonomnykh mnogoobrazii, VIII Mezhdunar. konkurs im. N. I. Lobachevskogo (1937), Otchët, Kazan. fiz.-mat. obsch-vo, Kazan, 1940, 327 pp.

[14] Vagner V. V., “Geometriya $(n-1)$-mernogo negolonomnogo mnogoobraziya v $n$-mernom prostranstve”, Tr. seminara po vektornomu i tenzornomu analizu, 5, Izd-vo Mosk. un-ta, M., 1941, 173–255 | MR

[15] Bejancu A., “Kähler contact distributions”, J. of Geometry and Physics, 60 (2010), 1958–1967 | DOI | MR | Zbl

[16] Vershik A. M., Gershkovich V. Ya., “Negolonomnye dinamicheskie sistemy. Geometriya raspredelenii i variatsionnye zadachi”, Itogi nauki i tekhniki. Ser. Sovrem. probl. mat. Fundamentalnye napravleniya, 16, VINITI, 1987, 5–85 | MR | Zbl

[17] Manin Yu. I., Kalibrovochnye polya i kompleksnaya geometriya, Nauka, M., 1984, 336 pp. | MR