A spectral condition determining the Kaehler property

Author:

Donnelly Harold

Abstract

We prove that the spectrum of the reduced complex Laplacian determines if a Hermitian manifold is Kaehler.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference6 articles.

1. Eigenvalues of the Laplacian;Berger, Marcel,1970

2. Harold Donnelly, Minakshisundaram’s coefficients on Kaehler manifolds, Proc. Sympos. Pure Math., vol. 27, Amer. Math. Soc., Providence, R. I. (to appear).

3. Spectral geometry and the Kaehler condition for complex manifolds;Gilkey, Peter B.;Invent. Math.,1974

4. An analytic proof of Riemann-Roch-Hirzebruch theorem for Kaehler manifolds;Patodi, V. K.;J. Differential Geometry,1971

5. Curvature and the eigenforms of the Laplace operator;Patodi, V. K.;J. Differential Geometry,1971

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1. Eigenvalues of the complex Laplacian on compact non-Kähler manifolds;Annals of Global Analysis and Geometry;2017-10-13

2. Spectral geometry of eta-Einstein Sasakian manifolds;Journal of Geometry and Physics;2012-11

3. Spectral geometry for almost isospectral hermitian manifolds;Geometriae Dedicata;1993-07

4. Hermitian natural differential operators;Lecture Notes in Mathematics;1986

5. Spektren symmetrischer Räume;Mathematische Nachrichten;1980

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