On generalized Gauduchon nilmanifolds

被引：4

作者：

Latorre, A. ^{[1
]}

Ugarte, L. ^{[2
]}

Villacampa, R. ^{[1
]}

机构：

[1] Acad Gen Mil, IUMA, Ctr Univ Def, Crta Huesca S-N, Zaragoza 50090, Spain

[2] Univ Zaragoza, IUMA, Dept Matemat, Campus Plaza San Francisco, E-50009 Zaragoza, Spain

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2017年 / 54卷

关键词：

Nilmanifold; Complex structure; Hermitian metrics; FILIFORM LIE-ALGEBRAS; COMPLEX STRUCTURES; TORSION METRICS; STRONG KAHLER; MANIFOLDS; EXISTENCE;

D O I：

10.1016/j.difgeo.2017.03.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct invariant generalized Gauduchon metrics on the product of two complex nilmanifolds that do not necessarily admit this kind of metrics. In particular, we prove that the product of a locally conformal Kaller nilmanifold and a balanced nilmanifold admits a generalized Gauduchon metric. In complex dimension 4, generalized Gauduchon nilmanifolds with (the highest possible) nilpotency step s = 5 are given, as well as 3-step and 4-step examples for which the center of their underlying Lie algebras does not contain any non-trivial J-invariant ideal. These examples show strong differences between the SKT and the generalized Gauduchon geometries of nilmanifolds. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：150 / 164

页数：15

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