Journal of Differential Geometry

The Metric Fibrations of Euclidean Space

Detlef Gromoll and Gerard Walschap


The purpose of this note is to complete the classification of metric fibrations in Euclidean space begun in [1]. Building on our techniques there, we show that regardless of dimension, the fibers are always the orbits of a free isometric group action by generalized glide rotations. A key ingredient of the argument is the fact that in the global setting, these fibrations satisfy a strong algebraic rigidity.

Article information

J. Differential Geom., Volume 57, Number 2 (2001), 233-238.

First available in Project Euclid: 20 July 2004

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Gromoll, Detlef; Walschap, Gerard. The Metric Fibrations of Euclidean Space. J. Differential Geom. 57 (2001), no. 2, 233--238. doi:10.4310/jdg/1090348110.

Export citation