Spectral theory of a class of nilmanifolds attached to Clifford modules

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Wolfram Bauer
  • Kenro Furutani
  • Chisato Iwasaki
  • Abdellah Laaroussi

Organisationseinheiten

Externe Organisationen

  • Osaka City University
  • University of Hyogo
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Details

OriginalspracheEnglisch
Seiten (von - bis)557-583
Seitenumfang27
FachzeitschriftMathematische Zeitschrift
Jahrgang297
Ausgabenummer1-2
PublikationsstatusVeröffentlicht - 3 Apr. 2020

Abstract

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.

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Spectral theory of a class of nilmanifolds attached to Clifford modules. / Bauer, Wolfram; Furutani, Kenro; Iwasaki, Chisato et al.
in: Mathematische Zeitschrift, Jahrgang 297, Nr. 1-2, 03.04.2020, S. 557-583.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Bauer, W, Furutani, K, Iwasaki, C & Laaroussi, A 2020, 'Spectral theory of a class of nilmanifolds attached to Clifford modules', Mathematische Zeitschrift, Jg. 297, Nr. 1-2, S. 557-583. https://doi.org/10.1007/s00209-020-02525-5
Bauer W, Furutani K, Iwasaki C, Laaroussi A. Spectral theory of a class of nilmanifolds attached to Clifford modules. Mathematische Zeitschrift. 2020 Apr 3;297(1-2):557-583. doi: 10.1007/s00209-020-02525-5
Bauer, Wolfram ; Furutani, Kenro ; Iwasaki, Chisato et al. / Spectral theory of a class of nilmanifolds attached to Clifford modules. in: Mathematische Zeitschrift. 2020 ; Jahrgang 297, Nr. 1-2. S. 557-583.
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abstract = "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.",
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AU - Bauer, Wolfram

AU - Furutani, Kenro

AU - Iwasaki, Chisato

AU - Laaroussi, Abdellah

N1 - Funding Information: The first and the last named author have been supported by the priority program SPP 2026 geometry at infinity of Deutsche Forschungsgemeinschaft (project number BA 3793/6-1), the second named author was supported by the Grant-in-aid for Scientific Research (C) No. 17K05284, JSPS; the third named author was supported by the Grant-in-aid for Scientific Research (C) No. 24540189, JSPS.

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AB - 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.

KW - Heat kernel

KW - Isospectral

KW - Pseudo H-type group

KW - Sub-Laplacian

KW - Subriemannian manifold

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