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Degeneration of plane affine Stolyarov connections

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Abstract

Consider a distribution of a plane in a projective space. A way of defining a plane affine Stolyarov connection associated with this distribution is proposed. It is set by the field of a connection object consisting of a connection quasitensor and a linear connection object. The object of this generalized affine connection defines torsion and curvature objects. We show that these objects are tensors. Conditions under which a plane affine Stolyarov connection is torsion-free or curvature-free are described. It is proved that the generalized affine connection with the connection quasitensor is the generalized Kronecker symbol degenerated into a linear connection.

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Authors and Affiliations

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

    Yu. I. Shevchenko

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  1. Yu. I. Shevchenko
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Correspondence to Yu. I. Shevchenko.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 16, No. 2, pp. 155–161, 2010.

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Shevchenko, Y.I. Degeneration of plane affine Stolyarov connections. J Math Sci 177, 753–757 (2011). https://doi.org/10.1007/s10958-011-0506-4

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  • DOI: https://doi.org/10.1007/s10958-011-0506-4

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