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Volume 2013 (2013), Article ID 902092, 9 pages
Darboux Transforms of a Harmonic Inverse Mean Curvature Surface
Division of Mathematics, Faculty of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba,
Ibaraki 305-8571, Japan
Received 18 December 2012; Accepted 17 February 2013
Academic Editor: Manuel Sanchis
Copyright © 2013 Katsuhiro Moriya. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- A. I. Bobenko, “Surfaces in terms of 2 by 2 matrices. Old and new integrable cases,” in Harmonic Maps and Integrable Systems, vol. 23 of Aspects of Mathematics, pp. 83–127, Friedrich Vieweg, Braunschweig, Germany, 1994.
- A. Sym, “Soliton surfaces and their applications (soliton geometry from spectral problems),” in Geometric Aspects of the Einstein Equations and Integrable Systems (Scheveningen, 1984), vol. 239 of Lecture Notes in Physics, pp. 154–231, Springer, Berlin, Germany, 1985.
- F. Pedit and U. Pinkall, “Quaternionic analysis on Riemann surfaces and differential geometry,” Documenta Mathematica, vol. 2, pp. 389–400, 1998, Proceedings of the International Congress of Mathematicians, Vol. 2, Berlin, Germany, 1998.
- C. Bohle, “Constrained Willmore tori in the 4-sphere,” Journal of Differential Geometry, vol. 86, no. 1, pp. 71–131, 2010.
- C. Bohle, K. Leschke, F. Pedit, and U. Pinkall, “Conformal maps from a 2-torus to the 4-sphere,” Journal für die Reine und Angewandte Mathematik, vol. 671, pp. 1–30, 2012.
- C. Bohle, F. Pedit, and U. Pinkall, “The spectral curve of a quaternionic holomorphic line bundle over a 2-torus,” Manuscripta Mathematica, vol. 130, no. 3, pp. 311–352, 2009.
- D. A. Korotkin, “On some integrable cases in surface theory,” in Differential Geometry, Lie Groups and Mechanics. Part 15-1, vol. 234 of Zapiski Nauchnykh Seminarov POMI, pp. 65–124, POMI, Saint Petersburg, Russia, 1996.
- A. Bobenko, U. Eitner, and A. Kitaev, “Surfaces with harmonic inverse mean curvature and Painlevé equations,” Geometriae Dedicata, vol. 68, no. 2, pp. 187–227, 1997.
- A. I. Bobenko and U. Eitner, Painlevé Equations in the Differential Geometry of Surfaces, vol. 1753 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2000.
- F. E. Burstall, D. Ferus, K. Leschke, F. Pedit, and U. Pinkall, Conformal Geometry of Surfaces in S4 and Quaternions, vol. 1772 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2002.
- K. Leschke and F. Pedit, “Bäcklund transforms of conformal maps into the 4-sphere,” in PDEs, Submanifolds and Affine Differential Geometry, vol. 69 of Banach Center Publications, pp. 103–118, Polish Academy of Sciences, Warsaw, Poland, 2005.
- K. Leschke and F. Pedit, “Sequences of Willmore surfaces,” Mathematische Zeitschrift, vol. 259, no. 1, pp. 113–122, 2008.
- E. Carberry, K. Leschke, and F. Pedit, “Darboux transforms and spectral curves of constant mean curvature surfaces revisited,” Annals of Global Analysis and Geometry, 2012.
- U. Hertrich-Jeromin and F. Pedit, “Remarks on the Darboux transform of isothermic surfaces,” Documenta Mathematica, vol. 2, pp. 313–333, 1997.
- G. Kamberov, F. Pedit, and U. Pinkall, “Bonnet pairs and isothermic surfaces,” Duke Mathematical Journal, vol. 92, no. 3, pp. 637–644, 1998.