Fiberwise homogeneous geodesic foliations of hyperbolic and Euclidean 3–spaces

Nuchi, Haggai

doi:10.2140/agt.2015.15.3059

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Fiberwise homogeneous geodesic foliations of hyperbolic and Euclidean $3$–spaces

Haggai Nuchi

Algebraic & Geometric Topology 15 (2015) 3057–3068

DOI: 10.2140/agt.2015.15.3059

Abstract

A fibration of a Riemannian manifold is fiberwise homogeneous if there are isometries of the manifold onto itself, taking any given fiber to any other one, and preserving fibers. In this paper, we describe all the fiberwise homogeneous fibrations of Euclidean and hyperbolic $3$ –space by geodesics. Our main result is that, up to fiber-preserving isometries, there is precisely a one-parameter family of such fibrations of Euclidean $3$ –space, and a two-parameter family in hyperbolic $3$ –space.

Keywords

homogeneous, geodesic, foliation, hyperbolic, Euclidean, 3-space

Mathematical Subject Classification 2010

Primary: 53C12

Secondary: 57R30, 57M60, 57S20

References

Publication

Received: 24 November 2014

Revised: 6 January 2015

Accepted: 20 February 2015

Published: 10 December 2015

Authors

Haggai Nuchi
Department of Mathematics University of Toronto Bahen Centre 40 George St, Room 6290 Toronto M5S 2E4 Canada

Volume 15, issue 5 (2015)