Hostname: page-component-848d4c4894-jbqgn Total loading time: 0 Render date: 2024-06-30T23:00:06.154Z Has data issue: false hasContentIssue false
  • English
  • Français

Projective submersions

Published online by Cambridge University Press:  17 April 2009

Fabio Podestà
Fabio Podestà
Affiliation:
Scuola Normale Superiore, P.zza Cavalieri, 1-56100 Pisa, Italy
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider C∞ manifolds endowed with torsionfree affine connections and C∞ projective submersions between them which, by definition, map geodesics into geodesics up to parametrisation. After giving a differential characterisation of these mappings, we deal with the case when one of the given connections is projectively flat or satisfies certain conditions concerning its Ricci tensor; under these hypotheses we prove that the projective submersion is actually a covering.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 2 , April 1991 , pp. 251 - 256
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Blumenthal, R.A., ‘Cartan submersions and Cartan foliations’, Illinois J. Math. 31 (1987), 327–343.Google Scholar
[2]Blumenthal, R.A., ‘Local isomorphisms of projective and conformal structures’, Geom. Dedicata, 16 (1984), 73–78.CrossRefGoogle Scholar
[3]Eisenhart, L.P., Non-Riemannian Geometry: Colloq. Publ. 8 (Amer. Math. Soc., 1927).Google Scholar
[4]Gray, A., ‘Einstein-like manifolds which are not Einstein’ Geom. Dedicata 7 (1978) 259–280.CrossRefGoogle Scholar
[5]Har'el, Z., ‘Projective mapping and distorsion theorems’ J. Diff. Geometry 15 (1980) 97–106.Google Scholar