Tohoku Mathematical Journal
2004
June
SECOND SERIES VOL. 56, NO. 2

Tohoku Math. J.
56 (2004), 179-204

Title SEMI-RIEMANNIAN SUBMERSIONS WITH TOTALLY GEODESIC FIBRES

Author Gabriel Bădiţoiu

(Received August 19, 2002, revised August 4, 2003)
Abstract. We classify semi-Riemannian submersions with connected totally geodesic fibres from a real pseudo-hyperbolic space onto a semi-Riemannian manifold under the assumption that the dimension of the fibres is less than or equal to three. Also, we obtain the classification of semi-Riemannian submersions with connected complex totally geodesic fibres from a complex pseudo-hyperbolic space onto a semi-Riemannian manifold under the assumption that the dimension of the fibres is less than or equal to two. We prove that there are no semi-Riemannian submersions with connected quaternionic fibres from a quaternionic pseudo-hyperbolic space onto a Riemannian manifold.

2000 Mathematics Subject Classification. Primary 53C50.
Key words and phrases. Semi-Riemannian submersions, isotropic semi-Riemannian manifolds, totally geodesic submanifolds, Ehresmann connections.

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