On Hodge decomposition and conformal variational problems

Details On Hodge decomposition and conformal variational problems On Hodge decomposition and conformal variational problems

2012-03-20

arxiv.org/abs/1203.4464v1

Mathematics

Differential Geometry

Scientific paper

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.

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