Generalized Killing spinors and conformal eigenvalue estimates for Spinc manifolds

被引：23

作者：

Herzlich, M ^{[1
]}

Moroianu, A ^{[1
]}

机构：

[1] Univ Montpellier 2, Dept Math, CNRS, UPRESE 5030, Montpellier, France

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 1999年 / 17卷 / 04期

关键词：

conformal eigenvalue estimates; Killing spinors; Spin(c) structures;

D O I：

10.1023/A:1006546915261

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we prove the Spin(c) analog of the Hijazi inequality on the first eigenvalue of the Dirac operator on compact Riemannian manifolds and study its equality case. During this study, we are naturally led to consider generalized Killing spinors on Spin(c) manifolds and we prove that such objects can only exist on low-dimensional manifolds (up to dimension three). This allows us to give a nice geometrical description of the manifolds satisfying the equality case of the above-mentioned inequality and to classify them in dimension three and four.

引用

页码：341 / 370

页数：30