On Hodge decomposition and conformal variational problems
Differential Geometry
2016-09-05 v1
Abstract
The main result is the identification of the orthogonal complement of the subalgebra of conformal vector field inside the algebra of all vector fields of a compact flat 2-manifold. As a fundamental tool, the complete Hodge decomposition for manifold with boundary is used. The identification allows the derivation of governing differential equations for variational problems on the space of conformal vector fields. Several examples are given. In addition, the paper also gives a review, in full detail, of already known vector field decompositions involving subalgebras of volume preserving and symplectic vector fields.
Keywords
Cite
@article{arxiv.1203.4464,
title = {On Hodge decomposition and conformal variational problems},
author = {Stephen Marsland and Robert McLachlan and Klas Modin and Matthew Perlmutter},
journal= {arXiv preprint arXiv:1203.4464},
year = {2016}
}