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Classification of multidimensional three-webs by closure conditions

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Abstract

Multidimensional three-webs are classified according to the type of identities holding in their coordinate loops. New identities and closure configurations connected with the fourth order differential neighborhood are considered. Along this path a number of problems of the theory of webs are solved. In particular, an algebraic interpretation is given of some structural tensors of the k-th order. A connection is established between the existence of automorphisms of coordinate loops of a web and the closedness of the g-structure defined by it.

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Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 21, pp. 109–154, 1989.

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Shelekhov, A.M. Classification of multidimensional three-webs by closure conditions. J Math Sci 55, 2140–2168 (1991). https://doi.org/10.1007/BF01095908

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Keywords

  • Fourth Order
  • Closure Condition
  • Structural Tensor
  • Closure Configuration
  • Algebraic Interpretation