FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 2, PAGES 155-161

Degeneration of plane affine Stolyarov connections

Yu. I. Shevchenko

Abstract

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In a projective space the plane distribution is considered. The way of the giving of plane affine Stolyarov's connection, associated with distribution, is offered. It is set by field of connection object consisting of connection quasitensor and linear connection object. The object of this generalized affine connection defines torsion and curvature objects. It is showed that these objects are tensors. Conditions when plane affine Stolyarov's connection is torsion free or curvature free are described. It is proved that the generalized affine connection with the connection quasitensor is the generalized Kroneker's symbol degenerates into linear connection.

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