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Submersions via Projections

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Abstract

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.

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References

  1. Gray, A.: Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16 (1967), 715-737.

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  2. O'Neill, B.: The fundamental equations of a submersion, Mich. Math. J. 13 (1966), 459-469.

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  3. Besse, A. L.: Einstein Manifolds, Chap. 9. Ergebnisse 3. Folge, Band 10, Springer-Verlag, Berlin, 1987.

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  1. Mathematisches Institut, Universität Bonn, Beringstr. 1, D-53115, Bonn, Germany

    H. Karcher

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  1. H. Karcher
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Karcher, H. Submersions via Projections. Geometriae Dedicata 74, 249–260 (1999). https://doi.org/10.1023/A:1005083115426

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  • DOI: https://doi.org/10.1023/A:1005083115426

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