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Nonexistence of skew loops on ellipsoids
Author(s):
Mohammad
Ghomi
Journal:
Proc. Amer. Math. Soc.
133
(2005),
3687-3690.
MSC (2000):
Primary 53A04, 53A05;
Secondary 53C45, 52A15
Posted:
June 3, 2005
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Abstract:
We prove that every  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.
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Additional Information:
Mohammad
Ghomi
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, Georia 30332
Address at time of publication:
Department of Mathematics, Penn State University, University Park, Pennsylvania 16802
Email:
ghomi@math.gatech.edu
DOI:
10.1090/S0002-9939-05-07933-5
PII:
S 0002-9939(05)07933-5
Keywords:
Tantrix,
skew loop,
ellipsoid,
quadric surface
Received by editor(s):
April 21, 2004
Received by editor(s) in revised form:
August 17, 2004
Posted:
June 3, 2005
Additional Notes:
The author's research was partially supported by NSF Grant DMS-0336455, and CAREER award DMS-0332333.
Communicated by:
Jon G. Wolfson
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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