A finiteness theorem for Riemannian submersions

Paweł G. Walczak

Annales Polonici Mathematici (1992)

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

Abstract

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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.

How to cite

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Paweł 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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  1. [A] M. T. Anderson, Convergence and rigidity of manifolds under Ricci curvature bounds, Invent. Math. 102 (1990), 429-445. Zbl0711.53038
  2. [AC] M. T. Anderson and J. Cheeger, Diffeomorphism finiteness for manifolds with Ricci curvature and L n / 2 -norm of curvature bounded, Geom. Funct. Anal. 1 (1991), 231-252. Zbl0764.53026
  3. [BK] P. Buser and H. Karcher, Gromov's almost flat manifolds, Astérisque 81 (1981), 1-148. Zbl0459.53031
  4. [C] J. Cheeger, Finiteness theorems for Riemannian manifolds, Amer. J. Math. 92 (1970), 61-74. Zbl0194.52902
  5. [Ep] D. B. A. Epstein, Transversally hyperbolic 1-dimensional foliations, Astérisque 116 (1984), 53-69. 
  6. [E] R. H. Escobales, Riemannian submersions with totally geodesic fibres, J. Differential Geom. 10 (1975), 253-276. Zbl0301.53024
  7. [GP] K. Grove and P. Petersen V, Bounding homotopy types by geometry, Ann. of Math. 128 (1988), 195-208. Zbl0655.53032
  8. [GPW] K. Grove, P. Petersen V and J.-Y. Wu, Geometric finiteness theorems via controlled topology, Invent. Math. 99 (1990), 205-213. Zbl0747.53033
  9. [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
  10. [M] P. Molino, Riemannian Foliations, Birkhäuser, Boston 1988. 
  11. [N] B. O'Neill, The fundamental equation of a submersion, Michigan Math. J. 13 (1966), 459-469. 
  12. [P] S. Peters, Cheeger's finiteness theorem for diffeomorphism classes of Riemannian manifolds, J. Reine Angew. Math. 349 (1984), 77-82. Zbl0524.53025
  13. [Rl] B. Reinhart, Foliated manifolds with bundle-like metrics, Ann. of Math. 69 (1959), 119-132. Zbl0122.16604
  14. [R2] B. Reinhart, The Differential Geometry of Foliations, Springer, Berlin 1983. 

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