一类环面的Khler度量

Khler Metric of a Kind of Torus

首先构造了利用无限循环群作用所形成的一类环面,此循环群异于环面的常见构造群;然后构造了此类环面的整体向量场;最后构造了此类环面的复结构和与此复结构相融的Khler度量,并利用此度量表示,Loewner环不等式和Loewner环收缩缺陷不等式给出了所构造环面中部分环面面积的下界.

Firstly,a kind of torus is constructed by the method of infinite cyclic group action which is different from general construction group of torus.Secondly,the global vector fields are constructed on the torus.Thirdly,one complex structure and one Khler metric which is harmonized with the complex structure are also constructed.Finally,the bottom bound of the area of some kind of torus is given by the Khler metric,Loewner＇s torus inequality and Loewner＇s torus inequality with isosystolic defect.