Tohoku Mathematical Journal

Semi-Riemannian submersions with totally geodesic fibres

Gabriel Bǎdițoiu

Full-text: Open access

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.

Article information

Source
Tohoku Math. J. (2), Volume 56, Number 2 (2004), 179-204.

Dates
First available in Project Euclid: 11 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1113246550

Digital Object Identifier
doi:10.2748/tmj/1113246550

Mathematical Reviews number (MathSciNet)
MR2053318

Zentralblatt MATH identifier
1061.53047

Subjects
Primary: 53C50: Lorentz manifolds, manifolds with indefinite metrics

Keywords
Semi-Riemannian submersions isotropic semi-Riemannian manifolds totally geodesic submanifolds Ehresmann connections

Citation

Bǎdițoiu, Gabriel. Semi-Riemannian submersions with totally geodesic fibres. Tohoku Math. J. (2) 56 (2004), no. 2, 179--204. doi:10.2748/tmj/1113246550. https://projecteuclid.org/euclid.tmj/1113246550


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