×

zbMATH — the first resource for mathematics

Surfaces obtained from \(\mathbb{C} \mathbb{P}^{N-1}\) sigma models. (English) Zbl 1165.37330
MSC:
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
53A05 Surfaces in Euclidean and related spaces
58E20 Harmonic maps, etc.
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Enneper A., Nachr. Königl. Gesell. Wissensch. Georg–Augusts-Univ. Göttingen 12 pp 258–
[2] K. Weierstrass, Mathematische Werke 3 (Verlagsbuchhandlung, Hillesheim, 1866) p. 219.
[3] DOI: 10.1007/BF02422217 · JFM 22.0766.05 · doi:10.1007/BF02422217
[4] DOI: 10.1007/BF02406731 · JFM 18.0425.01 · doi:10.1007/BF02406731
[5] Darboux G., Leçon sur la Thêorie des Surfaces (1887)
[6] Thomsen G., Abh. Math. Sem. Hamburg pp 31–
[7] DOI: 10.1007/PL00001392 · Zbl 0976.35064 · doi:10.1007/PL00001392
[8] DOI: 10.1016/S0393-0440(98)00018-7 · Zbl 0966.53042 · doi:10.1016/S0393-0440(98)00018-7
[9] DOI: 10.1007/BF02725619 · doi:10.1007/BF02725619
[10] DOI: 10.1007/978-3-663-14092-4_5 · doi:10.1007/978-3-663-14092-4_5
[11] DOI: 10.1017/CBO9781139174848 · doi:10.1017/CBO9781139174848
[12] DOI: 10.1007/978-3-0348-8330-6 · doi:10.1007/978-3-0348-8330-6
[13] DOI: 10.1017/CBO9780511543036 · doi:10.1017/CBO9780511543036
[14] Kenmotsu K., Surfaces with Constant Mean Curvatures (2003) · Zbl 1042.53001
[15] Osserman R., A Survey of Minimal Surfaces (1996) · Zbl 0209.52901
[16] DOI: 10.1088/0305-4470/29/6/012 · Zbl 0911.53007 · doi:10.1088/0305-4470/29/6/012
[17] DOI: 10.1002/sapm19969619 · Zbl 0869.58027 · doi:10.1002/sapm19969619
[18] DOI: 10.1111/1467-9590.00133 · Zbl 1002.37034 · doi:10.1111/1467-9590.00133
[19] DOI: 10.1063/1.532894 · Zbl 0967.53004 · doi:10.1063/1.532894
[20] DOI: 10.1088/0305-4470/39/29/013 · Zbl 1097.53005 · doi:10.1088/0305-4470/39/29/013
[21] DOI: 10.1016/j.geomphys.2005.03.003 · Zbl 1092.53044 · doi:10.1016/j.geomphys.2005.03.003
[22] Grundland A. M., J. Math. Phys. 46 pp 3508–
[23] DOI: 10.1111/j.1467-9590.2006.00358.x · Zbl 1145.58303 · doi:10.1111/j.1467-9590.2006.00358.x
[24] DOI: 10.1063/1.1586791 · Zbl 1062.58020 · doi:10.1063/1.1586791
[25] Gross D. J., Two-Dimensional Quantum Gravity and Random Surfaces (1992)
[26] DOI: 10.1103/PhysRevLett.67.1681 · Zbl 0990.81715 · doi:10.1103/PhysRevLett.67.1681
[27] Amit D., Field Theory, the Renormalization Group and Critical Phenomena (1978)
[28] Nelson D., Statistical Mechanics of Membranes and Surfaces (1992)
[29] DOI: 10.1007/978-1-4612-0883-9 · doi:10.1007/978-1-4612-0883-9
[30] Zakrzewski W. J., Low Dimensional Sigma Models (1989) · Zbl 0787.53072
[31] Zakharov V. E., Sov. Phys. 40 pp 1017–
[32] Helgason S., Differential Geometry, Lie Groups and Symmetric Spaces (1978)
[33] DOI: 10.1088/1751-8113/41/6/065204 · Zbl 1135.53041 · doi:10.1088/1751-8113/41/6/065204
[34] DOI: 10.1016/0550-3213(80)90291-6 · doi:10.1016/0550-3213(80)90291-6
[35] DOI: 10.1016/0370-2693(83)91065-1 · doi:10.1016/0370-2693(83)91065-1
[36] DOI: 10.1007/BF01458531 · Zbl 0642.53063 · doi:10.1007/BF01458531
[37] DOI: 10.1063/1.2815906 · Zbl 1153.81454 · doi:10.1063/1.2815906
[38] DOI: 10.1088/0305-4470/39/45/027 · Zbl 1105.81042 · doi:10.1088/0305-4470/39/45/027
[39] DOI: 10.1007/978-3-662-02414-0 · doi:10.1007/978-3-662-02414-0
[40] DOI: 10.1063/1.1337796 · Zbl 1016.53008 · doi:10.1063/1.1337796
[41] DOI: 10.1007/BF01573425 · doi:10.1007/BF01573425
[42] DOI: 10.1016/0550-3213(81)90568-X · doi:10.1016/0550-3213(81)90568-X
[43] DOI: 10.1103/PhysRevD.22.2006 · doi:10.1103/PhysRevD.22.2006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.