Advertisement

The metric foliations on Euclidean spaces

  • Llohann D. SperançaEmail author
  • Steffen Weil
Article

Abstract

We circumvent two gaps in the Gromoll–Walschap classification of metric fibrations from Euclidean spaces by presenting an alternative for the respective part of the proof. Combining it with the work of Florit–Goertsches–Lytchak–Töben, the classification of Riemannian foliations on Euclidean spaces is completed.

Keywords

Riemannian foliations Euclidean spaces 

Mathematics Subject Classification

53C20 53C12 

Notes

Acknowledgements

The authors thank A. Lytchak for his support and the anonymous referee for useful suggestions. The first named author is supported by Fundção de Amparo a Pesquisa do Estado de São Paulo, grant number 2017/19657-0, and Conselho Nacional de Pesquisa, grant number 404266/2016-9. He also would like to thank the University of Cologne for the hospitality. Part of this work is part of the Masters Thesis of the second named author.

References

  1. 1.
    Florit, L., Goertsches, O., Lytchak, A., Toeben, D.: Riemannian foliations on contractible manifolds. Muenster J. Math. 8, 1–16 (2015)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Gromoll, D., Walschap, G.: Metric fibrations in euclidean space. Asian J. Math. 1(4), 716–728 (1997)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Gromoll, D., Walschap, G.: The metric fibrations of euclidean space. J. Differ. Geom. 57(2), 233–238 (2001). 02MathSciNetCrossRefGoogle Scholar
  4. 4.
    Gromoll, D., Walshap, G.: Metric Foliations and Curvature. Birkhäuser, Basel (2009)CrossRefGoogle Scholar
  5. 5.
    Lytchak, A., Wilking, B.: Riemannian foliations of spheres. Geom. Topol. 20(3), 1257–1274 (2016)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Weil, S.: Metric foliations of space forms of nonnegative sectional curvature. Master thesis, Bonn (2010)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.I.C.T.-UnifespSão J. dos CamposBrazil
  2. 2.Bank VontobelZurichSwitzerland

Personalised recommendations