Dolbeault cohomology for G2-manifolds

被引：24

作者：

Fernandez, M ^{[1
]}

Ugarte, L ^{[1
]}

机构：

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

来源：

GEOMETRIAE DEDICATA | 1998年 / 70卷 / 01期

关键词：

G(2)-manifolds; vector cross-products; calibrated and cocalibrated G(2)-manifolds; G(2)-cohomology; compact G(2)-nilmanifolds;

D O I：

10.1023/A:1004940807017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Cocalibrated G(2)-manifolds are seven-dimensional Riemannian manifolds with a distinguished 3-form which is coclosed. For such a manifold M, S. Salamon in Riemannian Geometry and Holonomy Groups (Longman, 1989) defined a differential complex (A(q)(M),D-q(V)) related with the G(2)-structure of M. In this paper we study the cohomology H*(V)(M) of this complex; it is treated as an analogue of a Dolbeault cohomology of complex manifolds. For compact G(2)-manifolds whose holonomy group is a subgroup of G(2) special properties are proved. The cohomology H*(V)(Gamma/K) of any cocalibrated G(2)-nilmanifold Gamma\K is also studied.

引用

页码：57 / 86

页数：30