Natural differential operations on manifolds: An algebraic approachстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:The paper is devoted to the study of natural operations in differential geometry. Geometric objects over a manifold $M$ are interpreted as sections of natural bundles $\mathcal V\to M$ and natural operations are interpreted as the maps transforming sections of $\mathcal V\to M$ into sections of $\mathcal W\to M$. The authors describe a method for the description and classification of such operations, which reduces the original problem to equivariant maps between some jet spaces. The results are applied to natural operations between tensor bundles. Some natural operations on symplectic and Poisson manifolds are also studied.