The geodesics of metric connections with vectorial torsion

Details The geodesics of metric connections with vectorial torsion The geodesics of metric connections with vectorial torsion

2003-09-05

arxiv.org/abs/math/0309087v2

Mathematics

Differential Geometry

11 pages, with figures

Scientific paper

The present note deals with the dynamics of metric connections with vectorial torsion, as already described by E. Cartan in 1925. We show that the geodesics of metric connections with vectorial torsion defined by gradient vector fields coincide with the Levi-Civita geodesics of a conformally equivalent metric. By pullback, this yields a systematic way of constructing invariants of motion for such connections from isometries of the conformally equivalent metric, and we explain in as much this result generalizes the Mercator projection which maps sphere loxodromes to straight lines in the plane. An example shows that Beltrami's theorem fails for this class of connections. We then study the system of differential equations describing geodesics in the plane for vector fields which are not gradients, and show among others that the Hopf-Rinow theorem does also not hold in general.

Affiliated with

Also associated with

No associations

Rating

The geodesics of metric connections with vectorial torsion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The geodesics of metric connections with vectorial torsion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The geodesics of metric connections with vectorial torsion will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-358000