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Tr. Mat. Inst. Steklova, 2004, Volume 244, Pages 249–280 (Mi tm448)  

This article is cited in 11 scientific papers (total in 11 papers)

Dirac Operators and Conformal Invariants of Tori in 3-Space

I. A. Taimanov

Institute of Mathematics, Siberian Branch of USSR Academy of Sciences

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 $S^3$.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2004, 244, 233–263

Bibliographic databases:

UDC: 514.752.43+517.984
Received in April 2001

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, Tr. Mat. Inst. Steklova, 244, Nauka, MAIK Nauka/Inteperiodika, M., 2004, 249–280; Proc. Steklov Inst. Math., 244 (2004), 233–263

Citation in format AMSBIB
\Bibitem{Tai04}
\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 Tr. 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://www.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


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. A. Berdinskii, I. A. Taimanov, “Surfaces in three-dimensional Lie groups”, Siberian Math. J., 46:6 (2005), 1005–1019  mathnet  crossref  mathscinet  zmath  isi
    2. Taimanov I.A., “Finite-gap theory of the Clifford torus”, Int. Math. Res. Not., 2005, no. 2, 103–120  crossref  mathscinet  zmath  isi  elib
    3. I. A. Taimanov, “Two-dimensional Dirac operator and the theory of surfaces”, Russian Math. Surveys, 61:1 (2006), 79–159  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Taimanov I.A., “Surfaces in the four-space and the Davey–Stewartson equations”, J. Geom. Phys., 56:8 (2006), 1235–1256  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. 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  crossref  mathscinet  zmath  isi  scopus
    6. D. A. Berdinsky, “On constant mean curvature surfaces in the Heisenberg group”, Siberian Adv. Math., 22:2 (2012), 75–79  mathnet  crossref  mathscinet
    7. 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  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. McIntosh I., “The Quaternionic KP Hierarchy and Conformally Immersed 2-Tori in the 4-Sphere”, Tohoku Math J (2), 63:2 (2011), 183–215  crossref  mathscinet  zmath  isi  scopus
    9. 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  crossref  mathscinet  zmath  isi  elib  scopus
    10. Bohle Ch., Taimanov I.A., “Euclidean Minimal Tori With Planar Ends and Elliptic Solitons”, Int. Math. Res. Notices, 2015, no. 14, 5907–5932  crossref  mathscinet  zmath  isi  elib  scopus
    11. Bayard P., Lawn M.-A., Roth J., “Spinorial Representation of Submanifolds in Riemannian Space Forms”, Pac. J. Math., 291:1 (2017), 51–80  crossref  mathscinet  zmath  isi  scopus
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