A Family of Complex Nilmanifolds with in finitely Many Real Homotopy Types

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2017-12-21 DOI:10.1515/coma-2018-0004

A. Latorre, L. Ugarte, R. Villacampa

引用次数: 4

Abstract

Abstract We find a one-parameter family of non-isomorphic nilpotent Lie algebras ga, with a > [0,∞), of real dimension eight with (strongly non-nilpotent) complex structures. By restricting a to take rational values, we arrive at the existence of infinitely many real homotopy types of 8-dimensional nilmanifolds admitting a complex structure. Moreover, balanced Hermitian metrics and generalized Gauduchon metrics on such nilmanifolds are constructed.

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具有有限多个实同伦型的复零流形族

摘要研究了具有(强非幂零)复结构的实维8非同构幂零李代数群，它们具有>[0，∞]的单参数族。通过限制a取有理值，我们得到了具有复杂结构的8维零流形存在无穷多个实同伦类型。此外，还构造了这种零流形上的平衡厄米度量和广义高杜川度量。

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

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.