Kahler metrics of constant curvature on complex manifolds and topological invariants

复流形上常曲率的卡勒度量和拓扑不变量

• 批准号: 14540067
• 负责人: TSUBOI Kenji
• 金额: $ 1.73万
• 依托单位: Tokyo University of Marine Science & Technology (TUMST) (2004)東京水産大学 (2002-2003)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540067/
• 关键词: complex manifolds; Kahler metric of constant curvature; elliptic operator; group action; equivariant determinant; Bando-Calabi-Futaki invariant; fixed point set; rotation angle; 楕円型作用素; Futaki invariant; holonomy; 定曲率ケーラ計量

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.

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。

项目成果

The finite group action and the equivariant determinant of elliptic operators

椭圆算子的有限群作用和等变行列式

• 发表时间: 2005
• 期刊: J.Math.Soc.Japan Vol.57
• 作者: K.Tsuboi

A fixed point formula for compact complex manifolds

紧复流形的不动点公式

• 发表时间: 2002
• 期刊: J.Math.Kyoto Univ. Vol.42
• 作者: K.Tsuboi

K.Tsuboi: "Pseudo-free action of cyclic groups"Kokyuroku, RIMS, Kyoto Univ.. 1329. 26-35 (2003)

K.Tsuboi：“循环群的伪自由作用”Kokyuroku，RIMS，京都大学. 1329. 26-35 (2003)

A.Futaki, T.Mabuchi: "Moment maps and multilinear bilinear forms associated with symplectic classes"Asian J. Math. 6. 349-372 (2002)

A.Futaki、T.Mabuchi：“与辛类相关的矩图和多线性双线性形式”Asian J. Math。

The equivariant determinant of elliptic operators and the group action

椭圆算子的等变行列式和群作用

• 发表时间: 2004
• 期刊: Kokyuroku, RIMS, Kyoto Univ. 1387
• 作者: K.Tsuboi