Eigenvalues of the Kahlerian Dirac operator

被引：4

作者：

Bordoni, M

Hijazi, O

机构：

[1] Univ Roma La Sapienza, Dipartimento MeMoMat, I-00161 Rome, Italy

[2] Univ Nancy 1, Inst Elie Cartan, F-54506 Vandoeuvre Les Nancy, France

来源：

LETTERS IN MATHEMATICAL PHYSICS | 2001年 / 58卷 / 01期

关键词：

comparison of eigenvalues; Dirac operator; Kahler manifolds;

D O I：

10.1023/A:1012569607110

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We get estimates on the eigenvalues of the Kahlerian Dirac operator in terms of the eigenvalues of the scalar Laplace-Beltrami operator. In odd complex dimension, these estimates are sharp, in the sense that, for the first eigenvalue, they reduce to Kirchberg's inequality.

引用

页码：7 / 20

页数：14

共 12 条

[1] SPECTRAL ESTIMATES FOR SCHRODINGER AND DIRAC-TYPE OPERATORS ON RIEMANNIAN-MANIFOLDS [J].

BORDONI, M .

MATHEMATISCHE ANNALEN, 1994, 298 (04) :693-718

[2] THE CLASSIFICATION OF 4-DIMENSIONAL KAHLER-MANIFOLDS WITH SMALL EIGENVALUE OF THE DIRAC OPERATOR [J].

FRIEDRICH, T .

MATHEMATISCHE ANNALEN, 1993, 295 (03) :565-574

[3] THE 1ST EIGENVALUE OF THE DIRAC OPERATOR ON A COMPACT RIEMANNIAN MANIFOLD WITH NONNEGATIVE SCALAR-CURVATURE [J].

FRIEDRICH, T .

MATHEMATISCHE NACHRICHTEN, 1980, 97 :117-146

[4]

GALLOT S, 1988, ANN SCI ECOLE NORM S, V21, P561

[5] A CONFORMAL LOWER BOUND FOR THE SMALLEST EIGENVALUE OF THE DIRAC OPERATOR AND KILLING SPINORS [J].

HIJAZI, O .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1986, 104 (01) :151-162

[6] EIGENVALUES OF THE DIRAC OPERATOR ON COMPACT KAHLER-MANIFOLDS [J].

HIJAZI, O .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1994, 160 (03) :563-579

[7]

Kirchberg K. D., 1990, Journal of Geometry and Physics, V7, P449, DOI 10.1016/0393-0440(90)90001-J

[8] COMPACT 6-DIMENSIONAL KAHLER SPIN MANIFOLDS OF POSITIVE SCALAR CURVATURE WITH THE SMALLEST POSSIBLE 1ST EIGENVALUE OF THE DIRAC OPERATOR [J].

KIRCHBERG, KD .

MATHEMATISCHE ANNALEN, 1988, 282 (01) :157-176

[9]

KIRCHBERG KD, 1986, ANN GLOB ANAL GEOM, V4, P291

[10]

LAWSON HB, 1989, SPIN GEOMETRY

← 1 2 →