Killing forms on G2- and Spin7-manifolds

被引：14

作者：

Semmelmann, Uwe ^{[1
]}

机构：

[1] Univ Hamburg, Fachbereich Math, D-20146 Hamburg, Germany

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2006年 / 56卷 / 09期

关键词：

special holonomy manifolds; killing forms;

D O I：

10.1016/j.geomphys.2005.10.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Killing forms on Riemannian manifolds are differential forms whose covariant derivative is totally skew-symmetric. We prove that on a compact manifold with holonomy G(2) or Spin(7) any Killing form has to be parallel. The main tool is a universal Weitzenbock formula. We show, how such a formula can be obtained for any given holonomy group and any representation defining a vector bundle. (c) 2005 Published by Elsevier B.V.

引用

页码：1752 / 1766

页数：15

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