Nonexistence of skew loops on ellipsoids-Reference-Cited by-同舟云学术

Nonexistence of skew loops on ellipsoids

Published:2005-06-03 Issue:12 Volume:133 Page:3687-3690
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Ghomi Mohammad

Abstract

We prove that every C 1 C^1 closed curve immersed on an ellipsoid has a pair of parallel tangent lines. This establishes the optimal regularity for a phenomenon first observed by B. Segre. Our proof uses an approximation argument with the aid of an estimate for the size of loops in the tangential spherical image of a spherical curve.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2005-133-12/S0002-9939-05-07933-5/S0002-9939-05-07933-5.pdf

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