四维上的一个中心Kähler度量的共同源性

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2023-08-01 DOI:10.1515/advgeom-2023-0011

Thalia D. Jeffres, G. Maschler, Robert Ream

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引用次数: 0

摘要

摘要如果Kähler度量的Ricci自同态的行列式是常数，则称其为中心度量；参见[12]。对于这个常数为零的情况，我们在4-流形上研究了这类完全度量的存在性，这些度量对于三个单模三维李群具有上同根性1：SU（2），欧几里得平面运动的群E（2）和海森堡群nil3的离散子群的商。根据相关ODE系统的具体解，我们得到了SU（2）的一个完整分类，以及其他两组的一些存在性结果。

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Cohomogeneity one central Kähler metrics in dimension four

Abstract A Kähler metric is called central if the determinant of its Ricci endomorphism is constant; see [12]. For the case in which this constant is zero, we study on 4-manifolds the existence of complete metrics of this type which have cohomogeneity one for three unimodular 3-dimensional Lie groups: SU(2), the group E(2) of Euclidean plane motions, and a quotient by a discrete subgroup of the Heisenberg group nil3. We obtain a complete classification for SU(2), and some existence results for the other two groups, in terms of specific solutions of an associated ODE system.

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.