I. A. Taimanov, “Dirac Operators and Conformal Invariants of Tori in 3-Space”, Dynamical systems and related problems of geometry, Collected papers. Dedicated to the memory of academician Andrei Andreevich Bolibrukh, Trudy Mat. Inst. Steklova, 244, Nauka, MAIK «Nauka/Inteperiodika», M., 2004, 249–280; Proc. Steklov Inst. Math., 244 (2004), 233

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2004, Volume 244, Pages 249–280 (Mi tm448)

This article is cited in 13 scientific papers (total in 13 papers)

Dirac Operators and Conformal Invariants of Tori in 3-Space

I. A. Taimanov

Institute of Mathematics, Siberian Branch of USSR Academy of Sciences

Full-text PDF (377 kB) Citations (13)

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Abstract: 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

$S^3$ .

Received in April 2001

Bibliographic databases:

UDC: 514.752.43+517.984

Language: Russian

Citation: I. A. Taimanov, “Dirac Operators and Conformal Invariants of Tori in 3-Space”, Dynamical systems and related problems of geometry, Collected papers. Dedicated to the memory of academician Andrei Andreevich Bolibrukh, Trudy Mat. Inst. Steklova, 244, Nauka, MAIK «Nauka/Inteperiodika», M., 2004, 249–280; Proc. Steklov Inst. Math., 244 (2004), 233–263

Citation in format AMSBIB

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\by I.~A.~Taimanov

\paper Dirac Operators and Conformal Invariants of Tori in 3-Space

\inbook Dynamical systems and related problems of geometry

\bookinfo Collected papers. Dedicated to the memory of academician Andrei Andreevich Bolibrukh

\serial Trudy Mat. Inst. Steklova

\yr 2004

\vol 244

\pages 249--280

\publ Nauka, MAIK «Nauka/Inteperiodika»

\publaddr M.

\mathnet{http://mi.mathnet.ru/tm448}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2075118}

\zmath{https://zbmath.org/?q=an:1091.53041}

\transl

\jour Proc. Steklov Inst. Math.

\yr 2004

\vol 244

\pages 233--263

Linking options:

https://www.mathnet.ru/eng/tm448

https://www.mathnet.ru/eng/tm/v244/p249

This publication is cited in the following 13 articles:

V. A. Kyrov, “Poverkhnosti na psevdogelmgoltsevoi gruppe”, Matem. zametki, 117:2 (2025), 285–294
V. A. Kyrov, “Uravneniya Vaingartena dlya poverkhnostei na gruppakh gelmgoltseva tipa”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody kraevykh zadach. Pontryaginskie chteniya—XXXV», Voronezh, 26-30 aprelya 2024 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 235, VINITI RAN, M., 2024, 68–77
Bayard P., Lawn M.-A., Roth J., “Spinorial Representation of Submanifolds in Riemannian Space Forms”, Pac. J. Math., 291:1 (2017), 51–80
Bohle Ch., Taimanov I.A., “Euclidean Minimal Tori With Planar Ends and Elliptic Solitons”, Int. Math. Res. Notices, 2015, no. 14, 5907–5932
Alias L.J., de Lira J.H.S., Hinojosa J.A., “Generalized Weierstrass representation for surfaces in Heisenberg spaces”, Differential Geom Appl, 30:1 (2012), 1–12
de Lira J.H.S., Hinojosa J.A., “The Gauss map of minimal surfaces in the Anti-de Sitter space”, J Geom Phys, 61:3 (2011), 610–623
McIntosh I., “The Quaternionic KP Hierarchy and Conformally Immersed 2-Tori in the 4-Sphere”, Tohoku Math J (2), 63:2 (2011), 183–215
de Lira J.H.S., Hinojosa J.A., “The Gauss map of minimal surfaces in Berger spheres”, Ann. Global Anal. Geom., 37:2 (2010), 143–162
D. A. Berdinsky, “On constant mean curvature surfaces in the Heisenberg group”, Siberian Adv. Math., 22:2 (2012), 75–79
I. A. Taimanov, “Two-dimensional Dirac operator and the theory of surfaces”, Russian Math. Surveys, 61:1 (2006), 79–159
Taimanov I.A., “Surfaces in the four-space and the Davey–Stewartson equations”, J. Geom. Phys., 56:8 (2006), 1235–1256
D. A. Berdinskii, I. A. Taimanov, “Surfaces in three-dimensional Lie groups”, Siberian Math. J., 46:6 (2005), 1005–1019
Taimanov I.A., “Finite-gap theory of the Clifford torus”, Int. Math. Res. Not., 2005, no. 2, 103–120

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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