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Nonholonomic torses of the first kind

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Abstract

In the three-dimensional Euclidean space, we study two-dimensional nonholonomic distributions with zero total curvature of the first kind, called nonholonomic torses of the first kind. The two cases are considered: 1) one of the principal curvatures of the first kind differs from zero (the general case), 2) both of the principal curvatures of the first kind equal zero (a nonholonomic plane). The result obtained in the second case is of the general form. In the study we use the canonical moving frame and apply Cartan’s exterior forms method described by by S. P. Finikov in the book Cartan’s Exterior Forms Method in Differential Geometry (GITTL, Moscow-Leningrad, 1948).

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References

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Authors and Affiliations

  1. Tomsk State University, pr. Lenina 36, Tomsk, 634050, Russia

    O. V. Tsokolova

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  1. O. V. Tsokolova
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Correspondence to O. V. Tsokolova.

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Original Russian Text © O.V. Tsokolova, 2012, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, No. 3, pp. 51–61.

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Tsokolova, O.V. Nonholonomic torses of the first kind. Russ Math. 56, 45–54 (2012). https://doi.org/10.3103/S1066369X12030073

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  • DOI: https://doi.org/10.3103/S1066369X12030073

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