I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2010, VOLUME 16, NUMBER 2, PAGES 163-181
Lie jets and symmetries of prolongations of geometric objects
V. V. Shurygin
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The Lie jet of a field of
geometric objects on a smooth
with respect to a field of Weil -velocities is
a generalization of the Lie derivative of
a field with respect to
a vector field .
In this paper, Lie jets are applied to the
study of -smooth diffeomorphisms on a Weil bundle
of a smooth manifold , which are symmetries of
prolongations of geometric objects from to .
It is shown that vanishing of a Lie jet is
a necessary and sufficient condition for the prolongation
of a field of geometric
objects to be invariant with
respect to the transformation of the Weil bundle induced by
the field .
The case of symmetries of prolongations of fields of geometric objects
to the second-order tangent bundle are
considered in more detail.
Last modified: April 5, 2011