10 feb 2023 -- 14:30
Aula Seminari, DISMA, Politecnico di Torino
Differential Geometry Seminar Torino
Abstract.
The study of elastic curves (p=2) as well as their generalization to p-elastic curves is a central topic in differential geometry which goes back to the days of the Bernoulli family and L. Euler. In particular, free p-elastic curves (ie, critical points for compactly supported variations without constraining the length of the curves) arise in many different problems.
In the Euclidean plane, closed free p-elastic curves do not exist, but for a remarkable exception (namely, p=1). In the Euclidean sphere, the existence of closed free elastic curves (p=2) is well known. In this talk we show the existence of infinitely many closed free p-elastic curves for every 0<p<1, all of which are unstable. Using the theory of Killing vector fields along curves we will geometrically describe these curves and highlight an interesting evolution related to them.
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If you would like to attend the talk remotely, please send an e-mail to dgseminar.torino@gmail.com