论文标题
Weingarten表面的属性和转换
Properties and Transformations of Weingarten Surfaces
论文作者
论文摘要
从三个角度考虑了欧几里得3空间E3中旋转对称的表面满足的魏因丁关系：对脐点上关系斜率的限制，SL2（r）作为曲线空间上的分数线性变换的作用，以及关系的各种表述。关于第一个，我们根据脐点处的曲率半径的落下曲率下降，在魏因丁关系的斜率上获得边界。这概括了许多作者的最新工作。第二个，我们表明该动作从弯曲空间降至E3，并分为三个自然的几何作用。这将应用于一类称为半季度的Weingarten表面，该表面被证明是传递性的。最后，为建立的某些类型的Weingarten关系和稳定性提供了自然的拉格朗日公式。
The Weingarten relations satisfied by rotationally symmetric surfaces in Euclidean 3-space E3 are considered from three points of view: restrictions on the slope of the relation at umbilic points, the action of SL2(R) as fractional linear transformations on the space of curvatures, and variational formulations for the relations. With regard to the first, we obtain bounds on the slope of a Weingarten relation in terms of the fall off of the radii of curvature at an umbilic point. This generalizes recent work by a number of authors. For the second, we show that the action descends from curvature space to E3 and splits into three natural geometric actions. This is applied to a class of Weingarten surfaces, called semi-quadratic, on which the action is shown to be transitive. Finally, a natural Lagrangian formulation is given for certain types of Weingarten relations and stability established.
