Geometry of the exponential map(s) for nonlinear connections
by
L. Del Riego
Universidad Autónoma de San Luis Potosí, Mexico
Coauthors: Phillip E. Parker (Wichita State University)

Oral Communication

Over a pseudo-Riemmanian manifold one can always define a symmetric linear connection. Its exponential map is a local diffeomorphism and its Jacobi fields measure the geodesics' angular dispersion.

But this type of connections is not necessarily the best option for some spaces; for example, Finsler manifolds.

We have obtained analytical results on the exponential map(s) and the Jacobi fields for nonlinear connections, which measure not only angular but also longitudinal dispersion in the case of inhomogeneous connections. We were greatly aided by visualizing examples using Mathematica with a short program suggested by Alfred Gray. M. Mezzino improved it for the NextStep operating system, and P.E. Parker implemented a version for OS/2.

In this talk, we include examples of starlike neighborhoods and Jacobi fields for these nonlinear connections.

Date received: March 16, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadq-19.