Weierstrass Representation for Surfaces in the Three-Dimensional Heisenberg Group 被引量：1

Weierstrass Representation for Surfaces in the Three-Dimensional Heisenberg Group

导出

摘要 The authors define the Gauss map of surfaces in the three-dimensional Heisenberg group and give a representation formula for surfaces of prescribed mean curvature.Furthermore,a second order partial differential equation for the Gauss map is obtained,and it is shown that this equation is the complete integrability condition of the representation. The authors define the Gauss map of surfaces in the three-dimensional Heisenberg group and give a representation formula for surfaces of prescribed mean curvature. Furthermore, a second order partial differential equation for the Gauss map is obtained, and it is shown that this equation is the complete integrability condition of the representation.

作者 Qun CHEN Hongbing QIU

机构地区 School of Mathematics and Statistics Corresponding author. School of Mathematical Sciences

出处《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2010年第1期119-132,共14页 数学年刊（B辑英文版）

基金 supported by the National Natural Science Foundation of China (Nos. 10571068,10871149) the Research Fund for the Doctoral Program of Higher Education (No. 200804860046)

关键词三维表面海森堡群偏微分方程高斯映射可积性条件平均曲率曲面二阶 Heisenberg group, Mean curvature, Weierstrass representation

分类号 O174.22 [理学—基础数学] TP391.41 [自动化与计算机技术—计算机应用技术]

引文网络
相关文献

参考文献1

1Francesco MERCURI,StefanoMONTALDO,PaolaPIU.A Weierstrass Representation Formula for Minimal Surfaces in H_3 and H^2×R[J].Acta Mathematica Sinica,English Series,2006,22(6):1603-1612. 被引量：2

二级参考文献16

1Barbosa, J. L. M., Colares, A. G.: Minimal surfaces in R^3, Lecture Notes in Mathematics, 1195, Springer-Verlag, Berlin, 1986
2Gray, A.: Modern differential geometry of curves and surfaces with Mathematica, Second edition, CRC Press, Boca Raton, FL, 1998
3Bekkar, M.: Exemples de surfaces minimales dans l'espace de Heisenberg. Rend. Sem. Fac. Sci. Univ.Cagliari, 61, 123-130 (1991)
4Bekkar, M., Sari, T.: Surfaces minimales reglees dans l'espace de Heisenberg H3. Rend. Sem. Mat. Univ.Politec. Torino, 50, 243-254 (1992)
5Caddeo, R., Piu, P., Ratto, "A.: SO(2)-invariant minimal and constant mean curvature surfaces in 3-dimensional homogeneous spaces. Manuscripta Math., 87, 1-12 (1995)
6Figueroa, C. B., Mercuri, F., Pedrosa, R. H. L.: Invariant surfaces of the Heisenberg groups. Ann. Mat.Pura Appl., 177(4), 173-194 (1999)
7Piu, P., Sanini, A.: One-parameter subgroups and minimal surfaces in the Heisenberg group. Note Mat.,18, 143-153 (1998)
8Scott, D. P.: Minimal surfaces in the Heisenberg group, preprint
9Nelli, B., Rosenberg, H.: Minimal surfaces in H2 ×R. Bull. Braz. Math. Soc. (N.S.), 33, 263-292 (2002)
10Kokubu, M.: Weierstrass representation for minimal surfaces in hyperbolic space. Tohoku Math. J., 49,367-377 (1997)