Details
| Original language | English |
|---|---|
| Pages (from-to) | 557-583 |
| Number of pages | 27 |
| Journal | Mathematische Zeitschrift |
| Volume | 297 |
| Issue number | 1-2 |
| Publication status | Published - 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.
Keywords
- Heat kernel, Isospectral, Pseudo H-type group, Sub-Laplacian, Subriemannian manifold
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Mathematische Zeitschrift, Vol. 297, No. 1-2, 03.04.2020, p. 557-583.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Spectral theory of a class of nilmanifolds attached to Clifford modules
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.
PY - 2020/4/3
Y1 - 2020/4/3
N2 - 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.
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
UR - http://www.scopus.com/inward/record.url?scp=85083167178&partnerID=8YFLogxK
U2 - 10.1007/s00209-020-02525-5
DO - 10.1007/s00209-020-02525-5
M3 - Article
AN - SCOPUS:85083167178
VL - 297
SP - 557
EP - 583
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
IS - 1-2
ER -