Kahler metrics of constant curvature on complex manifolds and topological invariants

Futaki不变量阻碍了Kahler-Einstein度量的存在。本文给出了具有光纤F和基空间B的光纤束的Futaki不变量与Witten完整的关系，其中F是紧复流形，B是圆。这一结果发表在inK上。论爱因斯坦-卡勒度规和线束的完整性，《数学学报》。，卷45(2002),83-90。零、一维或三维球面具有群结构。本文利用该结构给出了紧致几乎复流形上有限群作用不动点数据的一个新公式。这一结果发表在inK上。Tsuboi，紧复流形的不动点公式，数学学报，Vol. 42(2002), 1-20。流形上的群作用表现了流形的对称性。在本研究中，我们发现了一种利用椭圆算子的等变行列式作为紧流形上有限群作用存在的阻碍的新方法。这一结果发表在inK上。李建平，椭圆算子的有限群作用和等变行列式，数学学报。日本，卷57(2005),95-113。

The Futaki invariant is an obstruction to the existence of Kahler-Einstein metrics. In this research we give an relation between the Futaki invariant and the Witten's holonomy of a fiber bundle with fiber F and base space B where F is a compact complex manifold and B is the circle. This result is published inK.Tsuboi, On the Einstein-Kahler metric and the holonomy of a line bundle, Proc.Edinburgh Math.Soc., Vol.45(2002), 83-90.The sphere of zero or one or three dimension have a group structure. In this research using this structure we give a new formula for the fixed point data of finite group action on compact almost complex manifolds. This result is published inK.Tsuboi, A fixed point formula for compact complex manifolds, J.Math.Kyoto Univ., Vol. 42 (2002), 1-20.Group action on manifolds represents the symmetry of manifolds. In this research we made a discovery of a new method to use the equivariant determinant of elliptic operators as an obstruction to the existence of finite group actions on compact manifolds. This result is published inK.Tsuboi, The finite group action and the equivariant determinant of elliptic operators, J.Math.Soc.Japan, vol.57 (2005), 95-113.