Semi-Riemannian submersions from real and complex pseudo-hyperbolic spaces. (English) Zbl 1036.53046

The authors classify semi-Riemannian submersions from a pseudo-hyperbolic space onto a Riemannian manifold under the assumption that the fibres are connected and totally geodesic. The index of the metric is kept unrestricted.
They present a large list of examples, and then they are able to prove a theorem, which says that this list is, in a well-defined sense, a complete one.


53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
Full Text: DOI arXiv


[1] P. Baird, J.C. Wood, Harmonic morphisms between Riemannian manifolds, London Math. Soc. Monogr. (N.S.), Oxford Univ. Press (to appear); P. Baird, J.C. Wood, Harmonic morphisms between Riemannian manifolds, London Math. Soc. Monogr. (N.S.), Oxford Univ. Press (to appear) · Zbl 1055.53049
[2] Besse, A. L., Einstein Manifolds (1987), Springer: Springer Berlin · Zbl 0613.53001
[3] Barros, M.; Romero, A., Indefinite Kähler manifolds, Math. Ann., 261, 55-62 (1982) · Zbl 0476.53013
[4] Coulton, P.; Glazebrook, J., Submanifolds of the Cayley projective plane with bounded second fundamental form, Geom. Dedicata, 33, 265-275 (1990) · Zbl 0698.53036
[5] Escobales, R., Riemannian submersions with totally geodesic fibers, J. Differential Geom., 10, 253-276 (1975) · Zbl 0301.53024
[6] Escobales, R., Riemannian submersions from complex projective spaces, J. Differential Geom., 13, 93-107 (1978) · Zbl 0406.53036
[7] Fuglede, B., Harmonic morphisms between semi-Riemannian manifolds, Ann. Acad. Sci. Fenn. Math., 21, 31-50 (1996) · Zbl 0847.53013
[8] Gray, A., Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech., 16, 715-737 (1967) · Zbl 0147.21201
[9] Ishihara, S., Quaternionic Kähler manifolds, J. Differential Geom., 9, 483-500 (1974) · Zbl 0297.53014
[10] Kwon, J. K.; Suh, Y. J., On sectional and Ricci curvatures of semi-Riemannian submersions, Kodai Math. J., 20, 53-66 (1997) · Zbl 0891.53016
[11] Lawson, H. B.; Michelsohn, M.-L., Spin Geometry (1989), Princeton Univ. Press: Princeton Univ. Press Princeton · Zbl 0688.57001
[12] Magid, M. A., Submersions from anti-de Sitter space with totally geodesic fibres, J. Differential Geom., 16, 323-331 (1981) · Zbl 0538.53061
[13] O’Neill, B., The fundamental equations of a submersion, Michigan Math. J., 13, 459-469 (1966) · Zbl 0145.18602
[14] O’Neill, B., Semi-Riemannian Geometry with Applications to Relativity (1983), Academic Press: Academic Press New York, London · Zbl 0531.53051
[15] Ranjan, A., Riemannian submersions of spheres with totally geodesics fibers, Osaka J. Math., 22, 243-260 (1985) · Zbl 0576.53035
[16] Wolf, J., Spaces of Constant Curvature (1967), McGraw-Hill: McGraw-Hill New York · Zbl 0162.53304
[17] Zhukova, N. I., Submersions with an Ehresmann connection, Izvestiya VUZ Matematika, 32, 25-33 (1988) · Zbl 0652.57018
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.