Abstract
A surjective submersion π: M→B from a pseudoriemannian manifold M is a fibre bundle, if its fibres are connected, totally geodesic and geodesically complete submanifolds of M.
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References
Besse, A.L.: Einstein manifolds. Berlin-Heidelberg-New York: Springer 1987
Blumenthal, R.A./ Hebda, J.J.: An analogue of the holonomy bundle for a foliated manifold. Tôhoku Math. J.40, 189–197 (1988)
Ehresmann, C.: Les connexions infinitésimales dans un expace fibré différentiable. Colloque de Topologie, Bruxelles 1951, 29–55
Hermann, R.: A sufficient condition that a mapping of Riemannian manifolds be a fibre bundle. Proc. Amer. Math. Soc.11, 236–242 (1960)
Kobayashi, S.: Transformation groups in differential geometry. Berlin-Heidelberg-New York: Springer 1972
Linden, M./ Reckziegel, H.: On the differentiability of maps into Lie transformation groups. manuscripta math.63, 377–379 (1989)
Poor, W.A.: Differential geometric structures. New York: McGraw-Hill 1981
Ponge, R./Reckziegel, H.: Twisted products in pseudoriemannian geometry. To appear in Geometriae Dedicata
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Reckziegel, H. A fiber bundle theorem. Manuscripta Math 76, 105–110 (1992). https://doi.org/10.1007/BF02567749
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DOI: https://doi.org/10.1007/BF02567749