Conformal invariant functionals of immersions of tori into R^3статья
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Дата последнего поиска статьи во внешних источниках: 22 декабря 2014 г.
Аннотация:We show, that higher analogs of the Willmore functional, defined on the space of immersions M^2 → R^3, where M^2 is a two-dimensional torus, R^3 is the three-dimensional Euclidean space are invariant under conformal transformations of R3. This hypothesis was formulated recently by I.A. Taimanov.
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.