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General relativity as a dynamical system on the manifold a of Riemannian metrics which cover diffeomorphisms

  • Arthur E. Fischer
  • Jerrold E. Marsden
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 14)

Keywords

Einstein Equation Riemannian Metrics Lapse Function Preserve Diffeomorphisms Open Convex Cone 
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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Bibliography

  1. 1.
    V. Arnold, Sur la géométrie differentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamique des fluids parfaits, Ann. Inst. Genoble 16 (1) (1966), 319–361.Google Scholar
  2. 2.
    R. Arnowitt, S. Deser and C. W. Misner, The Dynamics of General Relativity, in: Gravitation; An Introduction to Current Research, ed. L. Witten, Wiley, New York (1962).Google Scholar
  3. 3.
    B. DeWitt, Quantam Theory of Gravity. I. The Canonical Theory, Phys. Rev. 160 (1967), 1113–1148.Google Scholar
  4. 4.
    D. Ebin and J. Marsden, Groups of Diffeomorphisms and the Motion of an Incompressible Fluid, Ann. of Math. 92 (1970) 102–163.Google Scholar
  5. 5.
    A. Fischer and J. Marsden, The Einstein Equations of Evolution — A Geometric Approach, to appear.Google Scholar
  6. 6.
    A. Fischer and J. Marsden, The Geometry of the Einstein Evolution Equations, to appear.Google Scholar
  7. 7.
    S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Interscience (1963).Google Scholar
  8. 8.
    J. A. Wheeler, Geometrodynamics and the Issue of the Final State, in Relativity, Groups and Topology, ed. C. DeWitt and B. DeWitt, Gordon and Breach, New York (1964).Google Scholar

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • Arthur E. Fischer
    • 1
  • Jerrold E. Marsden
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeley

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