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Tensor structures on a differentiable manifold

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Summary

A tensor structure is a class of equivalent G-structures and it is defined by a special tensor field. Such fields are characterized by the existence of a linear connection relative to which they have covariant derivative zero. Two tensor structures may admit a common subordinate structure. Exaples of such subordinate stuctures are given and some cases, when one stucture is a Riemannian metric, are considered.

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To Enrico Bompiani on his scientific Jubilee

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Clark, R.S., Bruckheimer, M. Tensor structures on a differentiable manifold. Annali di Matematica 54, 123–141 (1961). https://doi.org/10.1007/BF02415347

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Keywords

  • Tensor Field
  • Tensor Structure
  • Linear Connection
  • Differentiable Manifold
  • Derivative Zero