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?
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Schueth, D. (2003). Constructing Isospectral Metrics via Principal Connections. In: Hildebrandt, S., Karcher, H. (eds) Geometric Analysis and Nonlinear Partial Differential Equations. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55627-2_4
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DOI: https://doi.org/10.1007/978-3-642-55627-2_4
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