Advertisement

Siberian Mathematical Journal

, Volume 35, Issue 1, pp 155–161 | Cite as

Curvature of the classical diffeomorphism groups

  • N. K. Smolentsev
Article

Keywords

Diffeomorphism Group Classical Diffeomorphism 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    N. K. Smolentsev, “Curvature of the diffeomorphism group and the space of volume elements,” Sibirsk. Mat. Zh.,33, No. 4, 135–141 (1992).Google Scholar
  2. 2.
    V. I. Arnol'd, Mathematical Methods in Classical Mechanics [in Russian], Nauka, Moscow (1974).Google Scholar
  3. 3.
    D. G. Ebin and J. Marsden, “Groups of diffeomorphisms and the motion of an incompressible fluid,” Matematika,17, No. 5 142–167; No. 6, 111–46 (1973).Google Scholar
  4. 4.
    A. M. Lukatskii, “Curvature of the group of diffeomorphisms preserving the measure of ann-dimensional torus,” Sibirsk. Mat. Zh.,25, 76–88 (1984).Google Scholar
  5. 5.
    A. M. Lukatskii, “Structure of the curvature tensor of the group of measure-preserving diffeomorphisms of a two-dimensional compact manifold,” Sibirsk. Mat. Zh.,29, No. 6 95–99 (1988).Google Scholar
  6. 6.
    T. Ratiu and R. Schmid, “The differentiable structure of three remarkable diffeomorphism groups,” Math. Z.,177, No. 1 81–100 (1981).Google Scholar
  7. 7.
    N. K. Smolentsev, “A bi-invariant metric on a group of symplectic diffeomorphisms and the equation ∂/∂δF=δF, F, Sibirsk. Mat. Zh.,27, No. 1 150–156 (1986).Google Scholar
  8. 8.
    D. E. Blair, Contact Manifolds in Riemannian Geometry, Springer, Berlin (1976).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • N. K. Smolentsev
    • 1
  1. 1.Kemerovo

Personalised recommendations