p-Kähler与具有幂零复结构的幂流形上的平衡结构

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2022-09-24 DOI:10.1007/s10455-022-09867-9

Tommaso Sferruzza, Nicoletta Tardini

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引用次数: 2

摘要

设（X，J）是具有不变幂零复结构的幂流形。我们研究了X上p-Kähler结构（包括Kächler和平衡度量）的存在性。更准确地说，我们确定了一个最优p，使得X上没有p-Kär结构。最后，我们证明了，与Käler情况相反，在紧致复流形上，平衡度量的存在性与Frölicher谱序列的退化阶之间没有关系。更准确地说，在平衡流形上，退化步长可以任意大。

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p-Kähler and balanced structures on nilmanifolds with nilpotent complex structures

Let (X, J) be a nilmanifold with an invariant nilpotent complex structure. We study the existence of p-Kähler structures (which include Kähler and balanced metrics) on X. More precisely, we determine an optimal p such that there are no p-Kähler structures on X. Finally, we show that, contrarily to the Kähler case, on compact complex manifolds there is no relation between the existence of balanced metrics and the degeneracy step of the Frölicher spectral sequence. More precisely, on balanced manifolds the degeneracy step can be arbitrarily large.

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来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.