Bour's theorem and helicoidal surfaces with constant mean curvature in the Bianchi-Cartan-Vranceanu spaces

带奇点的螺旋面的Bour定理

Bour's theorem for helicoidal surfaces with singularities

该研究推广Bour定理的技术，证明欧氏3维空间中螺旋运动不变的一般尖点棱、n型棱存在非平凡等距形变，并得出多个相关几何不变量为外蕴不变量的结论。

Bour's Theorem of Spacelike Surfaces in Minkowski 4--Space

In this paper, we study on three kinds of spacelike helicoidal surfaces in Minkowski $4$--space. First, we give an isometry between such helicoidal surfaces and rotational surfaces which is a kind of generalization of Bour theorem in Minkowski $3$--space to Minkowski $4$--space. Then, we investigate geometric properties for such isometric surfaces having same Gauss map. By using these results, we give the parametrizations of isometric pair of surfaces. As a particular case, we examine the right helicoidal surfaces in view of Bour's theorem. Also, we present some examples by choosing the compon…

Generalized Bour's theorem in Minkowski 3-space

We obtain isometric minimal helicoidal and rotational surfaces using generalized Bour's theorem in three dimensional Minkowski space. In addition, we show that the surfaces preserve minimality when their Gauss maps identically equal, choosing any diffentiable functions on the profile curve.

Isometric Surfaces and the Third Laplace-Beltrami

In this paper, classical isometric helicoidal and rotational surfaces are studied, and generalized by Bour's theorem in three dimensional Euclidean space. Moreover, the third Laplace-Beltrami operators of two classical surfaces are obtained.

四维闵氏空间中的等距类时螺旋面

Isometric Timelike Surfaces in 4--Dimensional Minkowski Space

本文研究四维闵氏空间中类时螺旋面的等距性质，分析其几何特性，并通过实例展示其参数化与可视化结果。