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Nonlinear mp-connectivities in principal fibrations

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Abstract

The paper deals with the multidimensional analog of the concept of nonlinear connectivity of order p, the content of the analog being that, for each m-submanifold of the basis of the principal fibration, there is defined a linear connectivity with horizontal m-distribution in the submanifolds passing through the common mP-element of tangency. It has been possible to reduce consideration to the case of a linear connectivity in the appropriately chosen principal fibration.

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Literature cited

  1. G. F. Laptev, “Manifolds embedded in generalized space,” in: Proceedings of the All-Union Mathematical Conference, 2, 226–233 [in Russian] (1964).

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  2. A. M. Vasil'ev, “Differential algebra as a tool of differential geometry,” in: Proceedings of the Geometry Seminar, 1, 33–61 [in Russian] (1966).

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  3. L. E. Evtushik, “Nonlinear connectivities of high order,” Izv. Vuzov. Matematika, No. 2, 32–44 (1969).

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    L. E. Evtushik

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  1. L. E. Evtushik
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Translated from Matematicheskie Zametki, Vol. 11, No. 3, pp. 341–351, March, 1972.

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Evtushik, L.E. Nonlinear mp-connectivities in principal fibrations. Mathematical Notes of the Academy of Sciences of the USSR 11, 211–216 (1972). https://doi.org/10.1007/BF01098528

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  • DOI: https://doi.org/10.1007/BF01098528

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