The first eigenvalue of the Dirac operator on locally reducible Riemannian manifolds

被引：8

作者：

Alexahdrov, Bogdan ^{[1
]}

机构：

[1] Univ Greifswald, Inst Math & Informat, D-17487 Greifswald, Germany

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2007年 / 57卷 / 02期

关键词：

Dirac operator; eigenvalue; killing spinor;

D O I：

10.1016/j.geomphys.2006.04.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a lower estimate for the first eigenvalue of the Dirac operator on a compact locally reducible Riemannian spin manifold with positive scalar curvature. We determine also the universal covers of the manifolds on which the smallest possible eigenvalue is attained. (c) 2006 Elsevier B.V. All rights reserved.

引用

页码：467 / 472

页数：6

共 50 条

[21] Spectra of the Dirac Operator of Pseudo-Riemannian Spin Manifolds
Momsen Reincke
Advances in Applied Clifford Algebras, 2017, 27 : 1675 - 1713
[22] The first eigenvalue of the Dirac operator in a conformal class
Ammann, Bernd
Humbert, Emmanuel
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2006, 3 (5-6) : 833 - 844
[23] Eigenvalue estimates for the Dirac operator on quaternionic Kähler manifolds
W. Kramer
U. Semmelmann
G. Weingart
Mathematische Zeitschrift, 1999, 230 : 727 - 751
[24] On the first eigenvalue of the p-Laplacian on Riemannian manifolds
Seto, Shoo
DIFFERENTIAL GEOMETRY AND GLOBAL ANALYSIS: IN HONOR OF TADASHI NAGANO, 2022, 777 : 199 - 209
[25] AN UPPER BOUND FOR THE 1ST EIGENVALUE OF THE DIRAC OPERATOR ON COMPACT RIEMANNIAN SPIN MANIFOLDS OF POSITIVE SCALAR CURVATURE
BAUM, H
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1990, 311 (06): : 389 - 392
[26] POSITIVE SCALAR CURVATURE AND THE DIRAC OPERATOR ON COMPLETE RIEMANNIAN-MANIFOLDS
GROMOV, M
LAWSON, HB
PUBLICATIONS MATHEMATIQUES, 1983, (58): : 295 - 408
[27] Upper bounds for the first eigenvalue of the Dirac operator on surfaces
Agricola, I
Friedrich, T
JOURNAL OF GEOMETRY AND PHYSICS, 1999, 30 (01) : 1 - 22
[28] An estimate for the first eigenvalue of the Dirac operator on compact Riemannian spin manifold admitting parallel one-form
Alexandrov, B
Grantcharov, G
Ivanov, S
JOURNAL OF GEOMETRY AND PHYSICS, 1998, 28 (3-4) : 263 - 270
[29] General formula for lower bound of the first eigenvalue on Riemannian manifolds
Chen, M
Wang, FY
SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY, 1997, 40 (04): : 384 - 394
[30] General formula for lower bound of the first eigenvalue on Riemannian manifolds
Chen, Mufa
Wang, Fengyu
Science in China, Series A: Mathematics, Physics, Astronomy, 40 (04): : 6 - 394

← 1 2 3 4 5 →