MATHEMATICA BOHEMICA, Vol. 124, No. 4, pp. 401-420 (1999)

Killing's equations in dimension two and
systems of finite type

G. Thompson

G. Thompson, Department of Mathematics, The University of Toledo, 2801 W. Bancroft St., Toledo, Ohio 43606, USA

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.

Keywords: Killing's equations, symmetric linear connections

Classification (MSC2000): 70H33, 53B05, 35A05

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