The Differential Calculus of Tensors

  • B. A. Dubrovin
  • A. T. Fomenko
  • S. P. Novikov
Part of the Graduate Texts in Mathematics book series (GTM, volume 93)


Most physical laws find mathematical expression as relationships between derivatives of one kind or another of various physical quantities. Many of these physical quantities are most appropriately represented as tensor (in particular vector) fields throughout space, or a region of space. We are therefore naturally interested in the question of what differential operations on tensors there exist, which are (in a sense to be made precise) independent of the co-ordinate system in terms of which we calculate their effect.


Vector Field Gaussian Curvature Curvature Tensor Transformation Rule Parallel Transport 
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Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • B. A. Dubrovin
    • 1
  • A. T. Fomenko
    • 2
  • S. P. Novikov
    • 3
  1. 1.c/o VAAP-Copyright Agency of the U.S.S.R.MoscowUSSR
  2. 2.3 Ya KaracharavskayaMoscowUSSR
  3. 3.L. D. Landau Institute for Theoretical PhysicsAcademy of Sciences of the U.S.S.R.MoscowUSSR

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