Proceedings of the International Conference on Geometry, Integrability and Quantization

Planar p-Elasticae and Rotational Linear Weingarten Surfaces

Álvaro Pámpano

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Abstract

We variationally characterize the profile curves of rotational linear Weingarten surfaces as planar p-elastic curves. Moreover, by evolving these planar p-elasticae under the binormal flow with prescribed velocity, we describe a procedure to construct all rotational linear Weingarten surfaces, locally. Finally, we apply our findings to two well-known family of surfaces.

Article information

Source
Proceedings of the Twentieth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Vladimir Pulov and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2019), 227-238

Dates
First available in Project Euclid: 21 December 2018

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1545361496

Digital Object Identifier
doi:10.7546/giq-20-2019-227-238

Mathematical Reviews number (MathSciNet)
MR3887753

Zentralblatt MATH identifier
1415.53002

Citation

Pámpano, Álvaro. Planar p-Elasticae and Rotational Linear Weingarten Surfaces. Proceedings of the Twentieth International Conference on Geometry, Integrability and Quantization, 227--238, Avangard Prima, Sofia, Bulgaria, 2019. doi:10.7546/giq-20-2019-227-238. https://projecteuclid.org/euclid.pgiq/1545361496


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