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

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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. 
@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},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2012_12_3_a2/}
}
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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/