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Conformal invariant functionals of immersions of tori into R^3

P. G. Grinevich·M. U. Schmidt
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Abstract

We show, that higher analogs of the Willmore functional, defined on the space of immersions M^2\rightarrow R^3, where M^2 is a two-dimensional torus, R^3 is the 3-dimensional Euclidean space are invariant under conformal transformations of R^3. This hypothesis was formulated recently by I.A.Taimanov (dg-ga/9610013). Higher analogs of the Willmore functional are defined in terms of the Modified Novikov-Veselov hierarchy. This soliton hierarchy is associated with the zero-energy scattering problem for the two-dimensional Dirac operator.

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P. G. Grinevich, M. U. Schmidt. 1997-02-17. Conformal invariant functionals of immersions of tori into R^3. https://doi.org/10.1016/s0393-0440(97)00038-7

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