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Annali di Matematica Pura ed Applicata

, Volume 54, Issue 1, pp 143–146 | Cite as

Some remarks on tensor differentiation

  • B. L. Foster
Article

Summary

The Jacobian of classical tensor analysis is generalized to a transformation operator containing second derivatives. This operator and the Jacobian may be used to formulate a second order tensor calculus. In this calculus, a simple contraction scheme includes as special cases Lie differentiation, the Lie bracket, covariant differentiation, and differentiation with respect to the tensor connections of Bompiani.

Keywords

Order Tensor Tensor Analysis Covariant Differentiation Transformation Operator Contraction Scheme 
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.

References

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    Vitali, G.,Geometria nello spazio hilbertiano, Zanichelli, Bologna, 1934.Google Scholar
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    Bompiani, E., Mem. Acad. Italia 6 (1935), pp. 269–520.zbMATHGoogle Scholar
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    Bompiani, E.,Le connessioni tensoriali, « Rend. Acc. dei Lincei », ser. VIII, vol. I, fasc. 5, pp. 478–482, (1946).MathSciNetGoogle Scholar
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    Cossu, A,Connessioni tensoriali per tensori doppi misti, « Rend. Acc dei Lincei », ser. VIII, vol. XIX, fasc. 6, pp. 421–427, (1955).MathSciNetGoogle Scholar

Copyright information

© Nicola Zanichelli Editore 1961

Authors and Affiliations

  • B. L. Foster
    • 1
  1. 1.SeattleU.S.A.

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