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On locally invariant affine connections. (English) Zbl 0746.53017
Webs and quasigroups. (“Nonlinear geometric algebra-89”), Tver’, 78-97 (1991).
[For the entire collection see Zbl 0742.00044.]
Details of some results due to P. Molino concerning locally invariant affine connections and Kostant’s theorem about rigid affine connections are given. The infinitesimal analog of an affine connection \(\nabla\) which is rigid with respect to a reductive connection \(\overline\nabla\) is defined. It is a tangent algebra of a special type. The tangent algebra defines an affine connection \(\nabla\) up to equivalence. Similar results are formulated for some manifolds of a special type.
53B05 Linear and affine connections