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Infinitesimal \(F\) -planar transformations. (English. Russian original) Zbl 1162.53008

Russ. Math. 52, No. 4, 13-18 (2008); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2008, No. 4, 16-22 (2008).
Let us consider a symmetric linear connection and \(F\), a tensor field of \((1,1)\)-type on a manifold \(A_n\). An infinitesimal transformation of \(A_n\) is called \(F\)-planar it it maps \(F\)-planar curves onto curves which are \(F\)-planar in their principal parts. The present paper is devoted to a study of these transformations considered as a generalization of infinitesimal geodesic transformations.
Reviewer: Radu Miron (Iaşi)

MSC:

53B05 Linear and affine connections
53B20 Local Riemannian geometry
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