Constructing Isospectral Metrics via Principal Connections

Dorothee Schueth ()
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Dorothee Schueth: Universität Bonn, Mathematisches Institut

A chapter in Geometric Analysis and Nonlinear Partial Differential Equations, 2003, pp 69-79 from Springer

Abstract: Abstract The spectrum of a closed Riemannian manifold is the eigenvalue spectrum of the associated Laplace operator acting on functions, counted with multiplicities; two manifolds are said to be isospectral if their spectra coincide. Spectral geometry deals with the mutual influences between the spectrum of a Riemannian manifold and its geometry. To which extent does the spectrum determine the geometry?

Keywords: Riemannian Manifold; Maximal Torus; Zariski Open Subset; Closed Riemannian Manifold; Canonical Action (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55627-2_4

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DOI: 10.1007/978-3-642-55627-2_4

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