ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

5. Differential Geometry and Global Analysis

1991 MS Classification: 53,58 Del Riego, Lilia, Universdad Autóma de San Luis Potosí, México; Parker, Phillip E., Wichita State University Exponential map for general sprays and connections An important class of systems of second order differential equations can be represented as generalized aprays on a manifold M with tangent bundle T M → M. Quadratic sprays correspond to symmetric linear connections on T M → M; and it is well known that the exponential map is a local diffeomorphism in this case. There is a corresponding set of locally diffeomorphic exponential maps that can be defined for any spray or connection, which satisfies certain properties, which we will discuss. A general Jacobi map will also be discussed. Reference: L. Del Riego, and Phillip E. Parker, Pseudoconvex and Disprisoning Connections, Preliminary Report.