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On conditions of coincidence of curvatures of the first and second types on distribution of planes

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Abstract

We consider distributions of planes in a multidimensional projective space and construct curvatures of the first and second types of group connections induced by composite equipments of the distributions. Conditions of coincidence of these curvatures are found. An internal composite equipment of a distribution of planes is performed. We prove that this equipment induces internal curvatures of the first and second types in the principal fiber bundle.

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References

  1. G. F. Laptev and N. M. Ostianu, “Distributions of m-dimensional linear elements in the space of projective connection, I,” Itogi Nauki Tekh. Ser. Probl. Geom. Tr. Geom. Sem., 3, 49–94 (1971).

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  3. O. M. Omelyan, “Four induced connections on planes distribution,” in: Int. Conf. on Geom. Analysis [in Russian], Penza (2003), pp. 63–69.

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  5. O. M. Omelyan, “On the coincidence of curvatures of the first and second types on distributions of planes,” in: Proc. Int. Conf. “Laptev readings—2009 [in Russian], Tver (2009), pp. 3.

  6. O. M. Omelyan, “Internal group connections on distribution,” Vestn. ChPGU im. I. J. Yakovleva, No. 5 (52), 120–125 (2006).

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Authors and Affiliations

  1. I. Kant Russian State University, Kaliningrad, Russia

    O. M. Omelyan

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  1. O. M. Omelyan
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Correspondence to O. M. Omelyan.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 16, No. 2, pp. 61–66, 2010.

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Omelyan, O.M. On conditions of coincidence of curvatures of the first and second types on distribution of planes. J Math Sci 177, 688–691 (2011). https://doi.org/10.1007/s10958-011-0497-1

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  • DOI: https://doi.org/10.1007/s10958-011-0497-1

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