Lower bounds for the eigenvalue estimates of the submanifold Dirac operator

被引：0
作者：
Yongfa Chen
机构：
[1] Central China Normal University,Department of Mathematics and Statistics
来源：
Mathematische Zeitschrift | 2021年 / 299卷
关键词：
Dirac operator; Eigenvalue; Mean curvature; Scalar curvature;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We get optimal lower bounds for the eigenvalues of the submanifold Dirac operator on locally reducible Riemannian manifolds in terms of intrinsic and extrinsic expressions. The limiting-cases are also studied. As a corollary, we can recover several known results in this direction.
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页码：2443 / 2460
页数：17
相关论文
共 22 条
  • [1] Alexandrov B(2007)The first eigenvalue of the Dirac operator on locally reducible Riemannian manifolds J. Geom. Phys. 57 467-472
  • [2] Alexandrov B(1998)An estimate for the first eigenvalue of the Dirac operator on compact Riemannian spin manifold admitting a parallel one-form J. Geom. Phys. 28 263-270
  • [3] Grantcharov G(1993)Real Killing spinors and holonomy Commun. Math. Phys. 154 509-521
  • [4] Ivanov S(2004)The first Dirac eigenvalues on manifolds with positive scalar curvature Proc. Am. Math. Soc. 132 3337-3344
  • [5] Bär C(2017)The Dirac operator on manifold admitting parallel one-form J. Geom. Phys. 117 214-221
  • [6] Bär C(1983)Positive mass theorems for black holes Commun. Math. Phys. 88 295-308
  • [7] Dahl M(2002)On eigenvalue estimate for the submanifold Dirac operator Int. J. Math. 13 533-548
  • [8] Chen Y(1998)The positive mass theorems for black holes revisited J. Geom. Phys. 26 97-111
  • [9] Gibbons G(1986)An estimation for the first eigenvalue of the Dirac operator in closed Kähler manifolds of positive scalar curvature Ann. Glob. Ann. Geom. 3 291-325
  • [10] Hawking S(1990)The first eigenvalue of the Dirac operator on Kähler manifolds J. Geom. Phys. 7 449-468
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