Compact nilmanifolds with nilpotent complex structures:: Dolbeault cohomology

被引：89

作者：

Cordero, LA ^{[1
]}

Fernández, M

Gray, A

Ugarte, L

机构：

[1] Univ Santiago de Compostela, Fac Matemat, Dept Geometria & Topol, Santiago De Compostela 15705, Spain

[2] Univ Basque Country, Fac Ciencias, Dept Matemat, Bilbao 48080, Spain

[3] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[4] Univ Zaragoza, Fac Ciencias, Dept Matemat Geometria & Topol, E-50009 Zaragoza, Spain

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2000年 / 352卷 / 12期

关键词：

D O I：

10.1090/S0002-9947-00-02486-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a special class of compact complex nilmanifolds, which we call compact nilmanifolds wit nilpotent complex structure. It is shown that if Gamma\G is a compact nilmanifold with nilpotent complex structure, then the Dolbeault cohomology H-<(partial derivative)over bar>*,* (Gamma\G) is canonically isomorphic to the <(partial derivative)over bar>-cohomology H-<(partial derivative)over bar>*,*(g(C)) of the bigraded complex (Lambda*,*(g(C))*, <(partial derivative)over bar>) of complex valued left invariant differential forms on the nilpotent Lie group G.

引用

页码：5405 / 5433

页数：29

共 33 条

[1]

Abbena E, 1997, B UNIONE MAT ITAL, V11B, P231

[2]

Atiyah M. F., 1957, T AM MATH SOC, V85, P181

[3] KAHLER AND SYMPLECTIC STRUCTURES ON NILMANIFOLDS [J].