BLASCHKE'S CURVATURE ENERGIES AND MINIMAL TORI IN S^3 - ALVARO PAMPANO - UNIVERSITY OF THE BASQUE COUNTRY

We introduce a curvature energy functional acting on planar curves of S3 which extends
a functional studied by Blaschke. Based on a technique involving Killing vector
fields, we show the existence of a biparametric family of closed critical curves for this
functional.
Next, using these closed critical curves as generators, we describe two constructions of
surfaces in S3, Hopf tori and binormal evolution tori, which give rise to closed tori critical
for a Blaschke’s type variational problem over surfaces and minimal tori of S3, respectively.
Finally, some properties of the critical generating curves are used to obtain results
about the tori.

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