Lie jets and symmetries of prolongations of geometric objects |
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Authors: | V V Shurygin |
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Institution: | 1.Kazan State University,Kazan,Russia |
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Abstract: | The Lie jet L
θ
λ of a field of geometric objects λ on a smooth manifold M with respect to a field θ of Weil A-velocities is a generalization of the Lie derivative L
v
λ of a field λ with respect to a vector field v. In this paper, Lie jets L
θ
λ are applied to the study of A-smooth diffeomorphisms on a Weil bundle T
A
M of a smooth manifold M, which are symmetries of prolongations of geometric objects from M to T
A
M. It is shown that vanishing of a Lie jet L
θ
λ is a necessary and sufficient condition for the prolongation λ
A
of a field of geometric objects λ to be invariant with respect to the transformation of the Weil bundle T
A
M induced by the field θ. The case of symmetries of prolongations of fields of geometric objects to the second-order tangent bundle T
2
M are considered in more detail. |
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Keywords: | |
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