Volume 15, issue 5 (2015)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Fiberwise homogeneous geodesic foliations of hyperbolic and Euclidean $3$–spaces

Haggai Nuchi

Algebraic & Geometric Topology 15 (2015) 3057–3068
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