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Closed G-structures on a differentiable manifold. (Russian. English summary) Zbl 0549.53032
Itogi Nauki Tekh., Ser. Probl. Geom. 7, 69-79 (1975).
Summary: The paper deals with G-structures of first order of finite type; the notion of closed G-structure is introduced. Such structures are characterized by the total formal integrability of the pseudo-Kählerian system of differential equations defining the structure. Examples of such structures are totally parallelizable structures, structures of Lie groups, and structures of symmetric spaces of affine connection. These structures also appear in the theory of three-webs formed by multidimensional surfaces on a differentiable manifold \(M^{2r}\). In particular, the structures associated with three-webs satisfying the Reidemeister and Bol condition are closed structures.

MSC:
53C10 \(G\)-structures
53A60 Differential geometry of webs