Tangent bundle geometry induced by second order partial differential equations
Differential Geometry
2023-07-20 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1412.2377,
title = {Tangent bundle geometry induced by second order partial differential equations},
author = {D. J. Saunders and O. Rossi and G. E. Prince},
journal= {arXiv preprint arXiv:1412.2377},
year = {2023}
}