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Journal of Mathematical Sciences

, 177:753 | Cite as

Degeneration of plane affine Stolyarov connections

  • Yu. I. Shevchenko
Article
  • 21 Downloads

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.

Keywords

Manifold Structural Equation Projective Space Linear Connection Plane Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.I. Kant State University of RussiaKaliningradRussia

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