Spectral theory of a class of nilmanifolds attached to clifford modules
| Autor: | Abdellah Laaroussi, Chisato Iwasaki, Kenro Furutani, Wolfram Bauer |
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| Rok vydání: | 2019 |
| Předmět: |
Mathematics - Differential Geometry
Class (set theory) Pure mathematics Spectral theory Trace (linear algebra) Mathematics::Dynamical Systems General Mathematics 01 natural sciences Mathematics - Spectral Theory 0103 physical sciences FOS: Mathematics Order (group theory) 0101 mathematics Mathematics::Symplectic Geometry Spectral Theory (math.SP) Mathematics 010102 general mathematics Spectrum (functional analysis) Zero (complex analysis) 58J53 58J50 Mathematics::Spectral Theory Isospectral Differential Geometry (math.DG) 010307 mathematical physics Mathematics::Differential Geometry Laplace operator |
| DOI: | 10.48550/arxiv.1911.02378 |
| Popis: | We determine the spectrum of the sub-Laplacian on pseudo H-type nilmanifolds and present pairs of isospectral but non-homeomorphic nilmanifolds with respect to the sub-Laplacian. We observe that these pairs are also isospectral with respect to the Laplacian. More generally, our method allows us to construct an arbitrary number of isospectral but mutually non-homeomorphic nilmanifolds. Finally, we present two nilmanifolds of different dimensions such that the short time heat trace expansions of the corresponding sub-Laplace operators coincide up to a term which vanishes to infinite order as time tends to zero. |
| Databáze: | OpenAIRE |
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