Computes differential invariants for conformal metrics.
problem Local recognition of conformal structures.
method Computes Hilbert polynomial and Poincare function.
result Resolves the local recognition problem for conformal structures.
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6 results for “jet-order”
We obtain the cohomology of the variational bicomplex on the infinite order jet space of a smooth fiber bundle in the class of exterior forms of finite jet order. This provides a solution of the global inverse problem of the calculus of variations of finite order on fiber bundles.
Defines a filtration on variational bicomplex for concise functional form conditions.
problem Expressing functional form vanishing conditions concisely.
method Introduces a filtration on the variational bicomplex and studies its properties.
result Graded components of the filtration inherit module structures, simplifying functional form conditions.
The action of a Lie pseudogroup on a smooth manifold induces a prolonged pseudogroup action on the jet spaces of submanifolds of . We prove in this paper that both the local and global freeness of the action of on persist under prolongation in the jet order . Our results underlie the const…
Researchers compute and describe differential invariants for self-dual conformal structures.
problem Local recognition problem for self-dual conformal structures.
method Quotient of self-duality equation, Hilbert polynomial, differential invariants, Poincaré function.
result Resolved the local recognition problem for self-dual conformal structures.
In this paper we classify Weingarten surfaces integrable in the sense of soliton theory. The criterion is that the associated Gauss equation possesses an sl(2)-valued zero curvature representation with a nonremovable parameter. Under certain restrictions on the jet order, the answer is given by a third order ordinary d…