Geometriae Dedicata

, Volume 74, Issue 3, pp 249–260 | Cite as

Submersions via Projections

  • H. Karcher


By writing the O'Neill tensors as derivatives of the natural projection one does not need the usual case distinctions any more and gets a much shorter list of basic equations. A short, induction free proof of the Frobenius theorem is a by-product.

submersion Frobenius theorem. 


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  1. 1.
    Gray, A.: Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16 (1967), 715-737.Google Scholar
  2. 2.
    O'Neill, B.: The fundamental equations of a submersion, Mich. Math. J. 13 (1966), 459-469.Google Scholar
  3. 3.
    Besse, A. L.: Einstein Manifolds, Chap. 9. Ergebnisse 3. Folge, Band 10, Springer-Verlag, Berlin, 1987.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • H. Karcher
    • 1
  1. 1.Mathematisches InstitutUniversität BonnBonnGermany

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