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Guijarro, Luis; Walschap, Gerard

Submetries vs. submersions. (English) Zbl 1235.53038

Rev. Mat. Iberoam. 27, No. 2, 605-619 (2011).
The authors study submetries between finite-dimensional Alexandrov spaces and show how some of the usual features of Riemannian submersions fail due to the Lack of smoothness. They give examples that show how some of the well-known splitting theorems for Riemannian submersions fail in the context of submetries. Also, they exhibit a submetry from a sphere with a locally flat metric everywhere except for a codimension one singular set.
Reviewer: Chiung-Jue Sung (Hsinchu)

Cited in 3 Documents

MSC:

53C20 Global Riemannian geometry, including pinching

Keywords:

Alexandrov spaces; submetry; quasigeodesics; extremal sets
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\textit{L. Guijarro} and \textit{G. Walschap}, Rev. Mat. Iberoam. 27, No. 2, 605--619 (2011; Zbl 1235.53038)
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References:

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