Details
| Original language | English |
|---|---|
| Pages (from-to) | 493-520 |
| Number of pages | 28 |
| Journal | Analysis and mathematical physics |
| Volume | 8 |
| Issue number | 4 |
| Publication status | Published - 1 Oct 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.
Keywords
- Hamilton’s equation, Killing vector fields, Pseudo-H-type nilmanifolds, Pseudo-Riemannian metric
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Algebra and Number Theory
- Mathematics(all)
- Mathematical Physics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Analysis and mathematical physics, Vol. 8, No. 4, 01.10.2018, p. 493-520.
Research output: Contribution to journal › Article › Research › 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 -