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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
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Abstract

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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

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