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Differential Operators on Smooth Manifolds

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Part of the Lecture Notes in Physics book series (LNP,volume 707)

Abstract

The property of a differential operator on a smooth manifold M to be invariant with respect to an action of some group G (especially a Lie group) on M plays a great role in mathematical physics since it helps select physically significant operators. The algebra DiffG(M) of all G-invariant differential operators with complex or real coefficients on M gives the material for constructing G-invariant physical theories on M. Properties of such theory are in close connection with properties of the algebra DiffG(M).

Keywords

  • Riemannian Manifold
  • Linear Subspace
  • Smooth Manifold
  • Isometry Group
  • Symmetric Operator

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.

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© 2006 Springer

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Shchepetilov, A.V. (2006). Differential Operators on Smooth Manifolds. In: Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces. Lecture Notes in Physics, vol 707. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-35386-0_2

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