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2001•Journal of the Korean Mathematical SocietyRequires access

ISOSPECTRAL MANIFOLDS WITH DIFFERENT LOCAL GEOMETRY

Carolyn S. Gordon

Open publisher page 5 citations

Abstract

Two compact Riemannian manifolds are said to be isospectral if the associated Laplace-Beltrami operators have the same eigenvalue spectrum. We describe a method, based on the used of Riemannian submersions, for constructing isospectral manifolds with different local geometry and survey examples constructed through this method.

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What this paper is about

Two compact Riemannian manifolds are said to be isospectral if the associated Laplace-Beltrami operators have the same eigenvalue spectrum. We describe a method, based on the used of Riemannian submersions, for constructing isospectral manifolds with different local geometry and survey examples constructed through this method.

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OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Two compact Riemannian manifolds are said to be isospectral if the associated Laplace-Beltrami operators have the same eigenvalue spectrum. We describe a method, based on the used of Riemannian submersions, for constructing isospectral manifolds with different local geometry and survey examples constructed through this method.

Key concepts: Isospectral, Mathematics, Spectral geometry, Riemannian geometry, Eigenvalues and eigenvectors, Pure mathematics, Spectrum (functional analysis), Mathematical analysis

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