Induced almost para-Kähler Einstein metrics on cotangent bundles

IF 0.6 4区 数学 Q3 MATHEMATICS
Andreas Čap, Thomas Mettler
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引用次数: 0

Abstract

In earlier work, we have shown that for certain geometric structures on a smooth manifold M of dimension n, one obtains an almost para-Kähler–Einstein metric on a manifold A of dimension 2n associated to the structure on M. The geometry also associates a diffeomorphism between A and $T^*M$ to any torsion-free connection compatible with the geometric structure. Hence we can use this construction to associate to each compatible connection an almost para-Kähler–Einstein metric on $T^*M$. In this short article, we discuss the relation of these metrics to Patterson–Walker metrics and derive explicit formulae for them in the cases of projective, conformal and Grassmannian structures.
共切束上的诱导几乎副卡勒爱因斯坦度量
在早先的工作中,我们已经证明,对于维数为 n 的光滑流形 M 上的某些几何结构,我们可以在维数为 2n 的流形 A 上得到一个与 M 上的结构相关联的近似对凯勒-爱因斯坦度量。因此,我们可以利用这一构造,在 $T^*M$ 上为每个兼容连接关联一个几乎准凯勒-爱因斯坦度量。在这篇短文中,我们将讨论这些度量与帕特森-沃克度量的关系,并推导出它们在投影结构、共形结构和格拉斯曼结构情况下的明确公式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
36
审稿时长
6-12 weeks
期刊介绍: The Quarterly Journal of Mathematics publishes original contributions to pure mathematics. All major areas of pure mathematics are represented on the editorial board.
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