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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Wang, L. -S. and Krishnaprasad, P. S. 1992. Gyroscopic control and stabilization. Journal of Nonlinear Science, Vol. 2, Issue. 4, p. 367.


    Bolder, H. 1969. Deformation of tensor fields described by time-dependent mappings. Archive for Rational Mechanics and Analysis, Vol. 35, Issue. 5, p. 321.


    Vaisman, Izu 1966. Sur quelques formules du calcul de Ricci global. Commentarii Mathematici Helvetici, Vol. 41, Issue. 1, p. 73.


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  • Proceedings of the Edinburgh Mathematical Society, Volume 12, Issue 1
  • June 1960, pp. 27-29

The Definition of Lie Derivative

  • T. J. Willmore (a1)
  • DOI: http://dx.doi.org/10.1017/S0013091500025013
  • Published online: 01 January 2009
Abstract

The differential operation known as Lie derivation was introduced by W. Slebodzinski in 1931, and since then it has been used by numerous investigators in applications in pure and applied mathematics and also in physics. A recent monograph by Kentaro Yano (2) devoted to the theory and application of Lie derivatives gives some idea of the wide range of its uses. However, in this monograph, as indeed in other treatments of the subject, the Lie derivative of a tensor field is defined by means of a formula involving partial derivatives of the given tensor field. It is then proved that the Lie derivative is a differential invariant, i.e. it is independent of a transformation from one allowable coordinate system to another. Sometimes some geometrical motivation is given in explanation of the formula, but this is seldom very satisfying.

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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