%0 Journal Article
%T Tangent bundle geometry induced by second order partial differential equations
%A D. J. Saunders
%A O. Rossi
%A G. E. Prince
%J Mathematics
%D 2014
%I arXiv
%X We show how the tangent bundle decomposition generated by a system of ordinary differential equations may be generalized to the case of a system of second order PDEs `of connection type'. Whereas for ODEs the decomposition is intrinsic, for PDEs it is necessary to specify a closed 1-form on the manifold of independent variables, together with a transverse local vector field. The resulting decomposition provides several natural curvature operators. The harmonic map equation is examined, and in this case both the 1-form and the vector field arise naturally.
%U http://arxiv.org/abs/1412.2377v2