On the flatness of Riemannian cylinders without conjugate points
Differential Geometry
2013-10-29 v2
Abstract
What are appropriate geometric conditions ensuring that a complete Riemannian 2-cylinder without conjugate points is flat? Examples with nonpositive curvature show that one has to assume that the ends of the cylinder open sublinearly. We show that sublinear growth of the ends is indeed sufficient if it is measured by the length of horocycles. This is used to extend results by K. Burns and G. Knieper [9], and by H. Koehler [18], where the opening of the ends is measured in terms of shortest noncontractible loops.
Keywords
Cite
@article{arxiv.1012.0659,
title = {On the flatness of Riemannian cylinders without conjugate points},
author = {Victor Bangert and Patrick Emmerich},
journal= {arXiv preprint arXiv:1012.0659},
year = {2013}
}
Comments
27 pages; v2: improved presentation in part (d) of the proof of Proposition 3.4, some stylistic changes; to appear in Communications in Analysis and Geometry