论文信息 - HELICOIDAL SURFACES WITH PRESCRIBED CURVATURES IN Nil3

HELICOIDAL SURFACES WITH PRESCRIBED CURVATURES IN Nil3

In the present paper, we study helicoidal surfaces in the 3-dimensional Heisenberg group Nil3. Also, we construct helicoidal surfaces in Nil3 with prescribed Gaussian curvature or mean curvature given by smooth functions. As the results, we classify helicoidal surfaces with constant Gaussian curvature or constant mean curvature.

[1] Katsuei Kenmotsu,et al. Surfaces of revolution with prescribed mean curvature , 1980 .

[2] P. Piu,et al. Rotational surfaces in H_3 with constant Gauss curvature , 1996 .

[3] I. I. Onnis,et al. Invariant surfaces of a three-dimensional manifold with constant Gauss curvature , 2005 .

[4] Ch. Delaunay,et al. Sur la surface de révolution dont la courbure moyenne est constante. , 1841 .

[5] Huili Liu,et al. Translation surfaces with constant mean curvature in 3-dimensional spaces , 1999 .

[6] Zhong Hua Hou,et al. Helicoidal surfaces under the cubic screw motion in Minkowski 3-space , 2006 .

[7] K. Nomizu,et al. Surfaces of revolution with constant mean curvature in Lorentz-Minkowski space , 1984 .

[8] Renato H. L. Pedrosa,et al. Invariant surfaces of the Heisenberg groups , 1999 .

[9] Christos Baikoussis,et al. Helicoidal surfaces with prescribed mean or Gaussian curvature , 1998 .

[10] George Kaimakamis,et al. Helicoidal surfaces in three-dimensional Minkowski space , 2002 .