Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 493-520 |
| Seitenumfang | 28 |
| Fachzeitschrift | Analysis and mathematical physics |
| Jahrgang | 8 |
| Ausgabenummer | 4 |
| Publikationsstatus | Veröffentlicht - 1 Okt. 2018 |
Abstract
Pseudo-H-type groups Gr , s form a class of step-two nilpotent Lie groups with a natural pseudo-Riemannian metric. In this paper the question of complete integrability in the sense of Liouville is studied for the corresponding (pseudo-)Riemannian geodesic flow. Via the isometry group of Gr , s families of first integrals are constructed. A modification of these functions gives a set of dim Gr , s functionally independent smooth first integrals in involution. The existence of a lattice L in Gr , s is guaranteed by recent work of K. Furutani and I. Markina. The complete integrability of the pseudo-Riemannian geodesic flow of the compact nilmanifold L\ Gr , s is proved under additional assumptions on the group Gr , s.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Algebra und Zahlentheorie
- Mathematik (insg.)
- Mathematische Physik
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in: Analysis and mathematical physics, Jahrgang 8, Nr. 4, 01.10.2018, S. 493-520.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - On the complete integrability of the geodesic flow of pseudo-H-type Lie groups
AU - Bauer, Wolfram
AU - Tarama, Daisuke
N1 - Funding Information: Wolfram Bauer: Partially supported by the DFG project BA 3793/6-1 in the framework of the SPP Geometry at infinity. Daisuke Tarama: Partially supported by JSPS KAKENHI Grant Number JP26870289. Publisher Copyright: © 2018, Springer Nature Switzerland AG. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2018/10/1
Y1 - 2018/10/1
N2 - Pseudo-H-type groups Gr , s form a class of step-two nilpotent Lie groups with a natural pseudo-Riemannian metric. In this paper the question of complete integrability in the sense of Liouville is studied for the corresponding (pseudo-)Riemannian geodesic flow. Via the isometry group of Gr , s families of first integrals are constructed. A modification of these functions gives a set of dim Gr , s functionally independent smooth first integrals in involution. The existence of a lattice L in Gr , s is guaranteed by recent work of K. Furutani and I. Markina. The complete integrability of the pseudo-Riemannian geodesic flow of the compact nilmanifold L\ Gr , s is proved under additional assumptions on the group Gr , s.
AB - Pseudo-H-type groups Gr , s form a class of step-two nilpotent Lie groups with a natural pseudo-Riemannian metric. In this paper the question of complete integrability in the sense of Liouville is studied for the corresponding (pseudo-)Riemannian geodesic flow. Via the isometry group of Gr , s families of first integrals are constructed. A modification of these functions gives a set of dim Gr , s functionally independent smooth first integrals in involution. The existence of a lattice L in Gr , s is guaranteed by recent work of K. Furutani and I. Markina. The complete integrability of the pseudo-Riemannian geodesic flow of the compact nilmanifold L\ Gr , s is proved under additional assumptions on the group Gr , s.
KW - Hamilton’s equation
KW - Killing vector fields
KW - Pseudo-H-type nilmanifolds
KW - Pseudo-Riemannian metric
UR - http://www.scopus.com/inward/record.url?scp=85057462358&partnerID=8YFLogxK
U2 - 10.1007/s13324-018-0250-8
DO - 10.1007/s13324-018-0250-8
M3 - Article
AN - SCOPUS:85057462358
VL - 8
SP - 493
EP - 520
JO - Analysis and mathematical physics
JF - Analysis and mathematical physics
SN - 1664-2368
IS - 4
ER -