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Einstein's evolution equation for the vacuum formulated on a space of differentials of immersions

Part I Non-linear Partial Differential Operators

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1037)

Keywords

  • Constraint Equation
  • Scalar Curvature
  • Tangent Vector
  • Tangent Bundle
  • Group Diff

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References

  1. Arnowitt, R., Deser, S., Misner, C., "The Dynamics of General Relativity in Gravitation, an Introduction to current research", L. Witten ed Wiley, New York, (1962)

    Google Scholar 

  2. Binz, E., "The Notion of Torsion and Second Fundamental Tensor Revisted", C.R.Math.Rep.Acad.Sci. Canada, Vol III/No 2, (1981)

    Google Scholar 

  3. Binz, E., "On the Levi-Civita Connection of a Gauged Levi-Civita Connection", C.R.Math.Rep.Acad.Sci., Canada, Vol IV/No 2, (1982)

    Google Scholar 

  4. Binz, E., Fischer, H.R., "The Manifold of Embeddings of a Closed Manifold", L.N.Math.Phys., 139, Springer-Verlag Berlin, Heidelberg, New York, (1978)

    Google Scholar 

  5. Bleecker, D., "Gauge Theory and Variational Principles", Addision Wesley Publ. Compl. Reading, Mass., (1981)

    MATH  Google Scholar 

  6. Choquet-Bruhat, Y., "The Problem of Constraints in General Relatively, Solution of the Lichnerowicz Equation", in Differential Geometry and Relativity, (A Volume in Honor of A. Lichnerowicz on his 60th Birthday), ed. by Cahen, M., and Flato, M., p. 225–235, D. Reidel Publ. Compl. Dordrecht, Holland, Boston, USA, (1976)

    CrossRef  Google Scholar 

  7. Francaviglia, M., "Applications of Infinite Dimensional Differential Geometry to General Relativity", Rev.Nuovo Cim., Vol/No 7, (1978)

    Google Scholar 

  8. Frölicher, A., Analyse Mathematique: "Applications lisses entre spaces et variétés de Fréchet", Université de Genève (1981)

    Google Scholar 

  9. Gutknecht, J., "Die C∞-Struktur auf der Diffeomorphismengruppe einer kompakten Mannigfaltigkeit", Diss. Nr. 5879, ETH-Zürich, (1979)

    Google Scholar 

  10. Golubitsky, M., Guillemin, V., "Stable Mappings and Their Singularities", Springer-Verlag Berlin, Heidelberg, New York, (1973)

    CrossRef  MATH  Google Scholar 

  11. Greub, W., Halperin, S., Vanstone, R., "Connections, Curvature Cohomology", Vol I, Academic Press, New York, London, (1972)

    Google Scholar 

  12. Hirsch, M.W., "Immersions of Manifolds", Trans.A.M.S. (93), p 243–276, (1959)

    Google Scholar 

  13. Keller, H.H., "Differential Calculus in Locally Convex Spaces", L.N.Math., 417, Springer-Verlag Berlin, Heidelberg, New York, (1974)

    Google Scholar 

  14. Lang, S., "Differential Manifolds", Addison Wesley Publ. Comp. Inc. Reading, Mass., (1972)

    MATH  Google Scholar 

  15. Lichnerowicz, A., "Propagateur et Commutateur en Relativité Génerale", Publ.Scientifiques, I H.E.S., Vol 10, (1961)

    Google Scholar 

  16. Marsden, J., "Application of Global Analysis in Mathematical Physics", Publish or Perish Inc., Boston, Mass., (1974).

    Google Scholar 

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Dedicated to H.H. Keller

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© 1983 Springer-Verlag Berlin Heidelberg

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Binz, E. (1983). Einstein's evolution equation for the vacuum formulated on a space of differentials of immersions. In: Andersson, S.I., Doebner, HD. (eds) Non-linear Partial Differential Operators and Quantization Procedures. Lecture Notes in Mathematics, vol 1037. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073168

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  • DOI: https://doi.org/10.1007/BFb0073168

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12710-9

  • Online ISBN: 978-3-540-38695-7

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