Lie Jets and Higher-Order Partial Connections

Abstract

© 2020, Springer Science+Business Media, LLC, part of Springer Nature. Higher-order partial connections are studied. We find conditions under which the Lie jet of a field of a geometric object ξ in the direction of the field of Weil A-velocities Y coincides with the covariant derivative ∇Yξ of this field with respect to some higher-order partial connection.