Kahler metrics of constant curvature on complex manifolds and topological invariants

Futaki不变量是Kahler-Einstein度规存在的障碍。本文给出了具有纤维F和基空间B的纤维丛的Futaki不变量与维滕完整性之间的关系，其中F是紧致复流形，B是圆.这一结果发表在K.Tsuboi，On the Einstein-Kahler metric and the holonomy of a line bundle，Proc.Edinburgh Math.Soc.，Vol.45（2002），83- 90.零维、一维或三维球面具有群结构。利用这种结构，我们给出了紧致几乎复流形上有限群作用的不动点数据的一个新公式。这个结果发表在K.Tsuboi，紧致复流形的不动点公式，J.Math.京都大学，42（2002），1- 20.流形上的群作用表示流形的对称性。在这项研究中，我们发现了一个新的方法，使用椭圆算子的等变行列式作为一个障碍，有限群作用的存在性紧流形。这个结果发表在K.Tsuboi，有限群作用和椭圆算子的等变行列式，J.Math.Soc.Japan，vol.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.