Killing's equations in dimension two and systems of finite type
Mathematica Bohemica (1999)
- Volume: 124, Issue: 4, page 401-420
- ISSN: 0862-7959
Access Full Article
top
Abstract
topHow to cite
topThompson, Gerard. "Killing's equations in dimension two and systems of finite type." Mathematica Bohemica 124.4 (1999): 401-420. <http://eudml.org/doc/248448>.
@article{Thompson1999,
abstract = {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.},
author = {Thompson, Gerard},
journal = {Mathematica Bohemica},
keywords = {Killing’s equations; symmetric linear connections; linear integrals of motion; system of finite type; quadratic integrals of motion; Killing's equations; symmetric linear connections; linear integrals of motion; system of finite type; quadratic integrals of motion},
language = {eng},
number = {4},
pages = {401-420},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Killing's equations in dimension two and systems of finite type},
url = {http://eudml.org/doc/248448},
volume = {124},
year = {1999},
}
TY - JOUR
AU - Thompson, Gerard
TI - Killing's equations in dimension two and systems of finite type
JO - Mathematica Bohemica
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 124
IS - 4
SP - 401
EP - 420
AB - 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.
LA - eng
KW - Killing’s equations; symmetric linear connections; linear integrals of motion; system of finite type; quadratic integrals of motion; Killing's equations; symmetric linear connections; linear integrals of motion; system of finite type; quadratic integrals of motion
UR - http://eudml.org/doc/248448
ER -
References
top- J. F. Pommaret, Systems of Partial Differential and Lie Pseudogroups, Gordon and Breach, New York, 1978. (1978) MR0517402
- G. Thompson, 10.1063/1.526114, J. Math. Phys. 25 (1984), 3474-3478. (1984) Zbl0549.70008MR0767554DOI10.1063/1.526114
- G. Thompson, 10.1063/1.527288, J. Math. Phys. 27(1986), 2693-2699. (1986) Zbl0607.53025MR0861329DOI10.1063/1.527288
- L. P. Eisenhart, Riemannian Geometry, Princeton University Press, 1925. (1925) MR1487892
- L. P. Eisenhart, Non-Riemannian Geometry, Amer. Math. Soc. Colloquium Publications 8, New York, 1927. (1927) MR1466961
- I. Anderson G. Thompson, The Inverse Problem of the Calculus of Variations for Ordinary differential Equations, Memoirs Amer. Math. Soc. 473, 1992. (1992) MR1115829
- J. Levine, Invariant characterizations of two dimensional affine and metric spaces, Duke Math. J. 15 (1948), 69-77. (1948) Zbl0029.41801MR0025236
- E. G. Kalnins W. Miller, 10.1137/0511089, SIAM J. Math. Anal. 11 (1980), 1011-1026. (1980) MR0595827DOI10.1137/0511089
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.