Differential geometric researches on surfaces in a space of constant curvature and their singularities

我们研究了常负曲率三维流形中的曲面，我们称之为双曲空间，从微分几何的观点出发，要求曲面具有良好的性质。(请注意，双曲线空间具有超出我们常识的有趣特征，例如，一条双曲线具有无限多个平行。)我们阐明了允许奇点的平面两端的渐近行为。对于线性Weingarten曲面，我们得到了一个整体表示式，奇点形状的判据，可方向性和共方向性等。

We studied surfaces in a three-dimensional manifold of constant negative curvature, called the hyperbolic space, requiring them to have good properties from the differential-geometric viewpoint. (Note that the hyperbolic space has interesting features beyond our common sense, e.g., a single hyperbolic line has infinitely many parallels.) We clarified the asymptotic behavior of ends of flat surfaces admitting singularities. Concerning linear Weingarten surfaces, we had a global representation formula, criterion for the shape of singularities, the orientability and co-orientability, and so on.