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Bundle of nilpotent Lie algebras over a nonholonomic manifold (nilpotentization)

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Abstract

On the tangent bundle of a nonholonomic manifold one defines a canonical structure of bundle of homogeneous nilpotent Lie algebras. On the local ring of a nonholonomic manifold one defines a quasijet structure. With the help of these constructions one uniformizes and simplifies a number of results of nonholonomic geometry.

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Authors
  1. A. M. Vershik
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  2. V. Ya. Gershkovich
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akad. Nauk SSSR, Vol. 172, pp. 21–40, 1989.

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Vershik, A.M., Gershkovich, V.Y. Bundle of nilpotent Lie algebras over a nonholonomic manifold (nilpotentization). J Math Sci 59, 1040–1053 (1992). https://doi.org/10.1007/BF01480685

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  • DOI: https://doi.org/10.1007/BF01480685

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