Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Accelerations of Riemannian quadratics

Author: Lyle Noakes
Journal: Proc. Amer. Math. Soc. 127 (1999), 1827-1836
MSC (1991): Primary 53B20, 53B99; Secondary 41A15, 41A29, 41A99
Published electronically: February 18, 1999
MathSciNet review: 1486744
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A Riemannian corner-cutting algorithm generalizing a classical construction for quadratics was previously shown by the author to produce a $C^1$ curve $p_\infty$ whose derivative is Lipschitz. The present paper takes the analysis of $p_\infty$ a step further by proving that it possesses left and right accelerations everywhere. Two-sided accelerations are shown to exist on the complement of a countable dense subset $D$ of the domain. The results are shown to be sharp in the following sense. For almost any scaled triple in Euclidean space there is a Riemannian perturbation of the Euclidean metric such that the two-sided accelerations of the resulting curve $p_\infty$ exist nowhere in $D$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 53B20, 53B99, 41A15, 41A29, 41A99

Retrieve articles in all journals with MSC (1991): 53B20, 53B99, 41A15, 41A29, 41A99

Additional Information

Lyle Noakes
Affiliation: Department of Mathematics, The University of Western Australia, Nedlands, Western Australia 6907, Australia

PII: S 0002-9939(99)04809-1
Keywords: Geodesic, parallel translation, corner-cutting
Received by editor(s): December 7, 1996
Received by editor(s) in revised form: June 11, 1997
Published electronically: February 18, 1999
Communicated by: Christopher Croke
Article copyright: © Copyright 1999 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia