Metric nonlinear connections

Details Metric nonlinear connections Metric nonlinear connections

2004-12-06

arxiv.org/abs/math/0412109v1

Differential Geometry and its Applications, 25 (2007), no. 3, 335--343

Mathematics

Differential Geometry

Scientific paper

10.1016/j.difgeo.2006.11.011

For a system of second order differential equations we determine a nonlinear connection that is compatible with a given generalized Lagrange metric. Using this nonlinear connection, we can find the whole family of metric nonlinear connections that can be associated with a system of SODE and a generalized Lagrange structure. For the particular case when the system of SODE and the metric structure are Lagrangian, we prove that the canonic nonlinear connection of the Lagrange space is the only nonlinear connection which is metric and compatible with the symplectic structure of the Lagrange space. The metric tensor of the Lagrange space determines the symmetric part of the nonlinear connection, while the symplectic structure of the Lagrange space determines the skew-symmetric part of the nonlinear connection.

Affiliated with

Also associated with

No associations

Rating

Metric nonlinear connections 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 Metric nonlinear connections, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Metric nonlinear connections will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-41100