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On Harmonic Differential Forms in a General Manifold

  • Nirmala Prakash

Abstract

During the past fifteen years the theory of form-calculus has been mainly responsible for the development of differential geometry. The roots of the subject are to be found in E. Cartan’s famous paper of 1934 on Finster spaces, and later on the subject flourished at the hands of S. Chern, J. A. Schouten, K. Kodiara, S. Bochner, A. Hilt, S. Hseiung, and several others.

Keywords

Hilbert Space Open Cover Harmonic Form Differentiable Manifold Topological Manifold 
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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References

  1. 1.
    J. R. Munkres, “Elementary Differential Topology,” Princeton University Press, Princeton, 1963.MATHGoogle Scholar
  2. 2.
    L. Auslander and R.E. Mackenzie, “Introduction to Differentiable Manifolds,” McGraw-Hill Book Co., New York, 1963.MATHGoogle Scholar
  3. 3.
    S. T. Hu, “Elements of General Topology,” Holden-Day-Inc., 1965.Google Scholar
  4. 4.
    S. I. Goldberg, “Curvature and Homology,” Academic Press, New York, 1962.MATHGoogle Scholar
  5. 5.
    N. Prakash, “Green’s Theorem in Noncompact Affine-Manifolds,” (to appear in National Instt. Sc. India).Google Scholar
  6. 6.
    J. Dieudonne, “Une Generalisation des espace compacts,” J. Math. Pures Appl. 23: (1944).Google Scholar
  7. 7.
    S. Lang, “Introduction to Differentiable Manifolds,” Interscience Publication, New York, (1962-63).MATHGoogle Scholar
  8. 8.
    J. Dieudonne, “Foundations of Modern Analysis,” Academic Press, New York, 1960.MATHGoogle Scholar
  9. 9.
    G. De. Rham, “Varietes differentiables,” Actualités scientifiques et industrielles, No. 1222, Herman, Paris, 1955.MATHGoogle Scholar
  10. 10.
    K. Yano, “Differential Geometry of Complex and Almost Complex Spaces, Pergamon Press, New York, 1965.Google Scholar
  11. 11.
    N. Prakash, “Green’s theorem in paracompact manifolds modeled on Hilbert spaces,” to appear in Proceedings of Indian Academy of Sciences.Google Scholar

Copyright information

© Plenum Press 1968

Authors and Affiliations

  • Nirmala Prakash
    • 1
  1. 1.Delhi UniversityDelhiIndia

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