Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 361-385 |
| Seitenumfang | 25 |
| Fachzeitschrift | Bulletin des Sciences Mathematiques |
| Jahrgang | 137 |
| Ausgabenummer | 3 |
| Publikationsstatus | Veröffentlicht - 24 Sept. 2012 |
| Extern publiziert | Ja |
Abstract
We classify the trivializable sub-Riemannian structures on odd-dimensional spheres SN that are induced by a Clifford module structure of RN+1. The underlying bracket generating distribution is of step two and spanned by a set of global linear vector fields X1, . . ., Xm. As a result we show that such structures only exist in the cases where N=3, 7, 15. The corresponding hypo-elliptic sub-Laplacians δsub are defined as the (negative) sum of squares of the vector fields Xj. In the case of a trivializable rank four distribution on S7 and a trivializable rank eight distribution on S15 we obtain a part of the spectrum of δsub. We also remark that in both cases there is a relation between the eigenfunctions and Jacobi polynomials.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
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in: Bulletin des Sciences Mathematiques, Jahrgang 137, Nr. 3, 24.09.2012, S. 361-385.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Trivializable sub-Riemannian structures on spheres
AU - Bauer, W.
AU - Furutani, K.
AU - Iwasaki, C.
N1 - Funding Information: * Corresponding author. Tel.: +49(0)551 397749; fax: +49(0)551 3922985. E-mail addresses: wbauer@uni-math.gwdg.de (W. Bauer), furutani_kenro@ma.noda.tus.ac.jp (K. Furutani), iwasaki@sci.u-hyogo.ac.jp (C. Iwasaki). 1 Supported by the DFG (Deutsche Forschungsgemeinschaft). 2 Supported by the “FY 2011 Researcher Exchange Program between JSPS and DAAD”. 3 Partially supported by the Grant-in-aid for Scientific Research (C) No. 20540218 of JSPS (Japan Society for the Promotion of Science). Copyright: Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2012/9/24
Y1 - 2012/9/24
N2 - We classify the trivializable sub-Riemannian structures on odd-dimensional spheres SN that are induced by a Clifford module structure of RN+1. The underlying bracket generating distribution is of step two and spanned by a set of global linear vector fields X1, . . ., Xm. As a result we show that such structures only exist in the cases where N=3, 7, 15. The corresponding hypo-elliptic sub-Laplacians δsub are defined as the (negative) sum of squares of the vector fields Xj. In the case of a trivializable rank four distribution on S7 and a trivializable rank eight distribution on S15 we obtain a part of the spectrum of δsub. We also remark that in both cases there is a relation between the eigenfunctions and Jacobi polynomials.
AB - We classify the trivializable sub-Riemannian structures on odd-dimensional spheres SN that are induced by a Clifford module structure of RN+1. The underlying bracket generating distribution is of step two and spanned by a set of global linear vector fields X1, . . ., Xm. As a result we show that such structures only exist in the cases where N=3, 7, 15. The corresponding hypo-elliptic sub-Laplacians δsub are defined as the (negative) sum of squares of the vector fields Xj. In the case of a trivializable rank four distribution on S7 and a trivializable rank eight distribution on S15 we obtain a part of the spectrum of δsub. We also remark that in both cases there is a relation between the eigenfunctions and Jacobi polynomials.
KW - Clifford algebra
KW - Jacobi polynomials
KW - Spectrum
KW - Sub-Laplacian
UR - http://www.scopus.com/inward/record.url?scp=84876704534&partnerID=8YFLogxK
U2 - 10.1016/j.bulsci.2012.09.004
DO - 10.1016/j.bulsci.2012.09.004
M3 - Article
AN - SCOPUS:84876704534
VL - 137
SP - 361
EP - 385
JO - Bulletin des Sciences Mathematiques
JF - Bulletin des Sciences Mathematiques
SN - 0007-4497
IS - 3
ER -