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The affine collineation of sinectic connection in a tangent bundle. (Russian) Zbl 0602.53014

The so-called ”sinectic connection” is a generalization of the well-known complete lift of a linear connection. The starting data of this paper are a manifold M, a sinectic connection on its tangent bundle and a vector field X: TM\(\to TTM\) described by their coordinate expressions. The author gives a local, tensorial criterion which guarantees that X induces an infinitesimal affine collineation of the sinectic connection considered. Some natural particular cases (when X is a projectable, horizontal, vertical or sinectic lift) are also discussed.
Reviewer: J.Szilasi

MSC:

53B15 Other connections
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