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Kinematics of tensor fields in hyperspace. II
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Geometry of hyperspace. I

J. Math. Phys. 17, 777 (1976); doi:10.1063/1.522976

Issue Date: May 1976

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Karel Kucha?
Department of Physics, University of Utah, Salt Lake City, Utah 84112
Hyperspace is heuristically defined as an (infinitely dimensional) manifold of all spacelike hypersurfaces embedded in a given Riemannian spacetime. The Riemannian structure ([script M],g) of spacetime induces a rich geometrical structure in hyperspace. Part of that structure, especially the moving normal frames in hyperspace, Lie derivatives, and symmetrical [del] and asymmetrical [del]* covariant hyperderivatives, are studied in detail. The formalism introduced in this paper sets the stage for the geometrical study of hypersurface kinematics and dynamics of general tensor fields with derivative gravitational coupling, and of the Dirac–ADM geometrodynamics with such tensor sources, in the following papers. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.
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KEYWORDS and PACS

Keywords
PACS
  • 02.40.Ky
    Mathematical methods in physics Geometry, differential geometry, and topology Riemannian geometries
  • 04.20.Cv
    Relativity and gravitation General relativity Fundamental problems and general formalism
  • 04.70.+t
    Relativity and gravitation Relativistic cosmology
  • YEAR: 1976

PUBLICATION DATA

ISSN:
0022-2488 (print)   1089-7658 (online)
Publisher:
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REFERENCES (7)
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  1. P. A. M. Dirac, Proc. R. Soc. London A 246, 326, 333 (1958);
  2. Phys. Rev. 114, 924 (1959);
    3. Lectures on Quantum Mechanics (Academic, New York, 1965).
  3. R. Arnowitt, S. Deser, and C. W. Misner, “The Dynamics of General Relativity,” in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962), and the original papers quoted there.
  4. For the geometrical approach to Hamiltonian geometrodynamics, see, e.g., A. E. Fisher and J. E. Marsden, J. Math. Phys. 13, 546 (1972).
  5. B. S. DeWitt, Phys. Rev. 160, 113 (1967);
    6. 162, 1195, 1239 (1967).
  6. K. Kuchař, J. Math. Phys. 13, 768 (1972).
  7. C. Teitelboim, Ann. Phys. 79, 542 (1973);
    8. K. Kuchař, “Canonical Quantization of Gravity,” in Relativity, Astrophysics and Cosmology, edited by W. Israel (Reidel, Dordrecht, Holland, 1974).
  8. S. A. Hojman, K. Kuchař, and C. Teitelboim, Nature 245, 97 (1973);
    9. K. Kuchař, J. Math. Phys. 15, 708 (1974).

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