Geodesic
On conditions of the coincidence of curvatures of the first and second types on distribution of planes
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 2, pp. 61-66.

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We consider distributions of planes in a multidimensional projective space and construct the curvatures of the first and second types of group connections induced by composite equipments of the distributions. Conditions of the coincidence of these curvatures are found. An internal composite equipment of a distribution of planes is performed. We prove that this equipment induces the internal curvatures of the first and second types in the principal fiber bundle. 
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O. M. Omelyan. On conditions of the coincidence of curvatures of the first and second types on distribution of planes. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 2, pp. 61-66. http://geodesic.mathdoc.fr/item/FPM_2010_16_2_a6/

[1] Laptev G. F., Ostianu N. M., “Raspredeleniya $m$-mernykh lineinykh elementov v prostranstve proektivnoi svyaznosti, I”, Itogi nauki i tekhn. Ser. Probl. geom. Tr. geom. sem., 3, 1971, 49–94 | MR

[2] Omelyan O. M., “Netenzornost ob'ekta krivizny gruppovoi svyaznosti na raspredelenii ploskostei”, Differentsialnaya geometriya mnogoobrazii figur, 33, 2002, 74–78 | MR | Zbl

[3] Omelyan O. M., “Chetyre indutsirovannykh svyaznosti na raspredelenii ploskostei”, Mezhdunar. konf. po geometrii i analizu, Penza, 2003, 63–69

[4] Omelyan O. M., “Puchki svyaznostei 1-go i 2-go tipov, indutsirovannye kompozitsionnym osnascheniem raspredeleniya ploskostei”, Dvizheniya v obobschënnykh prostranstvakh, Penza, 2005, 94–101

[5] Omelyan O. M., “O sovpadenii krivizn 1-go i 2-go tipov na raspredelenii ploskostei”, Tezisy dokladov mezhdunar. konf. “Laptevskie chteniya–2009”, Tver, 2009, 23

[6] Omelyan O. M., “Vnutrennie gruppovye svyaznosti na raspredelenii”, Vestnik ChPGU im. I. Ya. Yakovleva, 2006, no. 5(52), 120–125