Lower bounds for the eigenvalues of the Dirac operator: Part II. The submanifold Dirac operator

被引：21
|
作者：
Hijazi, O
Zhang, X
机构：
[1] Univ Nancy 1, Inst Elie Cartan, F-54506 Vandoeuvre Les Nancy, France
[2] Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100080, Peoples R China
来源：
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2001年 / 20卷 / 02期
基金：
中国国家自然科学基金;
关键词：
conformal geometry; Dirac operator; energy-momentum tensor; spectrum; submanifolds;
D O I：
10.1023/A:1011663603699
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we generalize the results of Part I to the submanifold Dirac operator. In particular, we give optimal lower bounds for the submanifold Dirac operator in terms of the mean curvature and other geometric invariants as the Yamabe number or the energy-momentum tensor. In the limiting case, we prove that the submanifold is Einstein if the normal bundle is flat.
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页码：163 / 181
页数：19
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