# A finiteness theorem for Riemannian submersions

Annales Polonici Mathematici (1992)

- Volume: 57, Issue: 3, page 283-290
- ISSN: 0066-2216

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topPaweł G. Walczak. "A finiteness theorem for Riemannian submersions." Annales Polonici Mathematici 57.3 (1992): 283-290. <http://eudml.org/doc/275915>.

@article{PawełG1992,

abstract = {Given some geometric bounds for the base space and the fibres, there is a finite number of conjugacy classes of Riemannian submersions between compact Riemannian manifolds.},

author = {Paweł G. Walczak},

journal = {Annales Polonici Mathematici},

keywords = {Riemannian foliation; Riemannian submersion; geometry bounds; finiteness; Riemannian foliations},

language = {eng},

number = {3},

pages = {283-290},

title = {A finiteness theorem for Riemannian submersions},

url = {http://eudml.org/doc/275915},

volume = {57},

year = {1992},

}

TY - JOUR

AU - Paweł G. Walczak

TI - A finiteness theorem for Riemannian submersions

JO - Annales Polonici Mathematici

PY - 1992

VL - 57

IS - 3

SP - 283

EP - 290

AB - Given some geometric bounds for the base space and the fibres, there is a finite number of conjugacy classes of Riemannian submersions between compact Riemannian manifolds.

LA - eng

KW - Riemannian foliation; Riemannian submersion; geometry bounds; finiteness; Riemannian foliations

UR - http://eudml.org/doc/275915

ER -

## References

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- [GPW] K. Grove, P. Petersen V and J.-Y. Wu, Geometric finiteness theorems via controlled topology, Invent. Math. 99 (1990), 205-213. Zbl0747.53033
- [HK] E. Heintze and H. Karcher, A general comparison theorem with applications to volume estimates for submanifolds, Ann. Sci. Ecole Norm. Sup. 11 (1978), 451-470. Zbl0416.53027
- [M] P. Molino, Riemannian Foliations, Birkhäuser, Boston 1988.
- [N] B. O'Neill, The fundamental equation of a submersion, Michigan Math. J. 13 (1966), 459-469.
- [P] S. Peters, Cheeger's finiteness theorem for diffeomorphism classes of Riemannian manifolds, J. Reine Angew. Math. 349 (1984), 77-82. Zbl0524.53025
- [Rl] B. Reinhart, Foliated manifolds with bundle-like metrics, Ann. of Math. 69 (1959), 119-132. Zbl0122.16604
- [R2] B. Reinhart, The Differential Geometry of Foliations, Springer, Berlin 1983.

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