Nonexistence of skew loops on ellipsoids
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- by Mohammad Ghomi PDF
- Proc. Amer. Math. Soc. 133 (2005), 3687-3690 Request permission
Abstract:
We prove that every $C^1$ 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.References
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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
- MR Author ID: 687341
- Email: ghomi@math.gatech.edu
- Received by editor(s): April 21, 2004
- Received by editor(s) in revised form: August 17, 2004
- Published electronically: 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 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 3687-3690
- MSC (2000): Primary 53A04, 53A05; Secondary 53C45, 52A15
- DOI: https://doi.org/10.1090/S0002-9939-05-07933-5
- MathSciNet review: 2163608