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.
@article{1113246550,
author = {B\v adi\c toiu, Gabriel},
title = {Semi-Riemannian submersions with totally geodesic fibres},
journal = {Tohoku Math. J. (2)},
volume = {56},
number = {1},
year = {2004},
pages = { 179-204},
language = {en},
url = {http://dml.mathdoc.fr/item/1113246550}
}
Bǎdițoiu, Gabriel. Semi-Riemannian submersions with totally geodesic fibres. Tohoku Math. J. (2), Tome 56 (2004) no. 1, pp. 179-204. http://gdmltest.u-ga.fr/item/1113246550/