Geometry of nonlinear connections

We show that locally diffeomorphic exponential maps can be defined for any second-order differential equation, and give a (possibly nonlinear) covariant derivative for any (possibly nonlinear) connection. We introduce vertically homogeneous connections as the natural correspondents of homogeneous se...

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Bibliographic Details
Published in:Nonlinear analysis 2005-11, Vol.63 (5), p.e501-e510
Main Authors: Riego, L. Del, Parker, Phillip E.
Format: Article
Language:English
Subjects:
Geodesics
Nonlinear connection
Nonlinear covariant derivative
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Summary:We show that locally diffeomorphic exponential maps can be defined for any second-order differential equation, and give a (possibly nonlinear) covariant derivative for any (possibly nonlinear) connection. We introduce vertically homogeneous connections as the natural correspondents of homogeneous second-order differential equations. We provide significant support for the prospect of studying nonlinear connections via certain, closely associated second-order differential equations. One of the most important is our generalized Ambrose-Palais-Singer correspondence.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2004.09.002