论文标题
圆环上可集成指标的变形刚度
Deformational rigidity of integrable metrics on the torus
论文作者
论文摘要
据推测，二维曲线上唯一的集成指标是liouville指标。在本文中，我们研究了这种猜想的变形版本：我们考虑了一个相结合类中非灯泡liouville指标的可整合变形，并表明，对于相当大的此类变形，变形指标再次是liouville。由于我们的证明方法会立即延续到更高的尺寸托里，因此在这种更一般的情况下，我们获得了类似的陈述。为了将我们的结果置于角度，我们回顾了有关圆环上可集成指标的现有结果。
It is conjectured that the only integrable metrics on the two-dimensional torus are Liouville metrics. In this paper, we study a deformative version of this conjecture: We consider integrable deformations of a non-flat Liouville metric in a conformal class and show that for a fairly large class of such deformations the deformed metric is again Liouville. Since our method of proof immediately carries over to higher dimensional tori, we obtain analogous statements in this more general case. In order to put our results in perspective, we review existing results about integrable metrics on the torus.
