The metric foliations on Euclidean spaces


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.

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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.

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Correspondence to Llohann D. Sperança.

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Sperança, L.D., Weil, S. The metric foliations on Euclidean spaces. Math. Z. 295, 1295–1299 (2020).

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  • Riemannian foliations
  • Euclidean spaces

Mathematics Subject Classification

  • 53C20
  • 53C12