Geodesic
Dirac Operators and Conformal Invariants of Tori in 3-Space
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems and related problems of geometry, Tome 244 (2004), pp. 249-280

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It is proved that the multipliers of the Floquet functions that are associated with immersions of tori into $\mathbb R^3$ (or $S^3$) form a complex curve in $\mathbb C^2$. The properties of this curve are studied. In addition, it is shown how the curve and its construction are related to the method of finite-gap integration, the Willmore functional, and harmonic mappings of the 2-torus into $S^3$. 
@article{TM_2004_244_a9,
     author = {I. A. Taimanov},
     title = {Dirac {Operators} and {Conformal} {Invariants} of {Tori} in {3-Space}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {249--280},
     publisher = {mathdoc},
     volume = {244},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2004_244_a9/}
}
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I. A. Taimanov. Dirac Operators and Conformal Invariants of Tori in 3-Space. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems and related problems of geometry, Tome 244 (2004), pp. 249-280. http://geodesic.mathdoc.fr/item/TM_2004_244_a9/