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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.
##### MSC:
 53B05 Linear and affine connections
##### Keywords:
rigid affine connection; tangent algebra