Vector fields and connections on TM. (English) Zbl 0722.53019

One problem of great interest in modern geometry is the connection between objects on the total space of a tangent bundle TM and objects on the base M. For example, every spray on a smooth manifold M determines a linear connection without torsion on TM. The author considers the problem of the geometrical construction of connections on TM by a vector field on M, using first order natural procedures. He characterizes the set of such vector fields and constructs all natural differential operators of first order from this set into the space of all connections on TM.


53C05 Connections (general theory)
58A20 Jets in global analysis
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