The hat theorem and problems of classification of structures on Riemannian manifolds (Q1397573)

This paper is devoted to \(G\)-structures on Riemannian manifolds, where \(G\subset \text{O}(n)\). The tensor \(h=\nabla -\overline\nabla\) is investigated, where \(\nabla\) and \(\overline\nabla\) are the covariant derivatives generated by the initial Riemannian metric and the \(G\)-structure under consideration, respectively. This tensor is applied to classify \(G\)-structures at a point of a manifold. It is proved that a \(G\)-structure belongs to different classes at different points in general.