| Title:
|
Killing's equations in dimension two and systems of finite type (English) |
| Author:
|
Thompson, G. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
124 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
401-420 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A PDE system is said to be of finite type if all possible derivatives at some order can be solved for in terms lower order derivatives. An algorithm for determining whether a system of finite type has solutions is outlined. The results are then applied to the problem of characterizing symmetric linear connections in two dimensions that possess homogeneous linear and quadratic integrals of motions, that is, solving Killing's equations of degree one and two. (English) |
| Keyword:
|
Killing’s equations |
| Keyword:
|
symmetric linear connections |
| Keyword:
|
linear integrals of motion |
| Keyword:
|
system of finite type |
| Keyword:
|
quadratic integrals of motion |
| MSC:
|
34A26 |
| MSC:
|
35A05 |
| MSC:
|
53B05 |
| MSC:
|
53Z05 |
| MSC:
|
70G45 |
| MSC:
|
70H33 |
| idZBL:
|
Zbl 0952.70014 |
| idMR:
|
MR1722875 |
| DOI:
|
10.21136/MB.1999.125998 |
| . |
| Date available:
|
2009-09-24T21:39:15Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125998 |
| . |
| Reference:
|
[1] J. F. Pommaret: Systems of Partial Differential and Lie Pseudogroups.Gordon and Breach, New York, 1978. MR 0517402 |
| Reference:
|
[2] G. Thompson: Polynomial constants of motion in a flat space.J. Math. Phys. 25 (1984), 3474-3478. Zbl 0549.70008, MR 0767554, 10.1063/1.526114 |
| Reference:
|
[3] G. Thompson: Killing tensors in spaces of constant curvature.J. Math. Phys. 27(1986), 2693-2699. Zbl 0607.53025, MR 0861329, 10.1063/1.527288 |
| Reference:
|
[4] L. P. Eisenhart: Riemannian Geometry.Princeton University Press, 1925. MR 1487892 |
| Reference:
|
[5] L. P. Eisenhart: Non-Riemannian Geometry.Amer. Math. Soc. Colloquium Publications 8, New York, 1927. MR 1466961 |
| Reference:
|
[6] I. Anderson G. Thompson: The Inverse Problem of the Calculus of Variations for Ordinary differential Equations.Memoirs Amer. Math. Soc. 473, 1992. MR 1115829 |
| Reference:
|
[7] J. Levine: Invariant characterizations of two dimensional affine and metric spaces.Duke Math. J. 15 (1948), 69-77. Zbl 0029.41801, MR 0025236 |
| Reference:
|
[8] E. G. Kalnins W. Miller: Killing tensors and variable separation for Hamilton-Jacobi and Helmholtz equations.SIAM J. Math. Anal. 11 (1980), 1011-1026. MR 0595827, 10.1137/0511089 |
| . |
