李群紧凑商上的 p-Kähler 结构注释

IF 1 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2024-03-21 DOI:10.1007/s10231-024-01438-y

Anna Fino, Asia Mainenti

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引用次数: 0

摘要

复维度为 n 的复流形上的 p-Kähler 结构是由 d 封闭横实数（p，p）形式给出的。在本文中，我们将研究简单相连的李群的离散子群在具有不变复结构的紧凑商上的 p-Kähler 结构的存在性。特别是，我们讨论了零曼弗雷德上 p-Kähler 结构的存在，重点是 \(p =2\) 和复维度 \(n = 4\) 的情况。此外，我们还证明了一个复维度为（n＝3）的（（(n-2)\）-Kähler近似阿贝尔索曼菲尔德必须是Kähler的。

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A note on p-Kähler structures on compact quotients of Lie groups

A p-Kähler structure on a complex manifold of complex dimension n is given by a d-closed transverse real (p, p)-form. In the paper, we study the existence of p-Kähler structures on compact quotients of simply connected Lie groups by discrete subgroups endowed with an invariant complex structure. In particular, we discuss the existence of p-Kähler structures on nilmanifolds, with a focus on the case \(p =2\) and complex dimension \(n = 4\). Moreover, we prove that a \((n-2)\)-Kähler almost abelian solvmanifold of complex dimension \(n\ge 3\) has to be Kähler.

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来源期刊

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it). A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.