In this paper, we present geometrical interpretations of the Lie derivative and the Lie-invariance for an affine connection, based on two geometrical constructions: the former is given on the tangent bundle and relies on the notion of linear Ehresmann connection; the latter is developed on the frame bundle and is based on the more common notion of principal connection.
On the Lie derivative of an affine connection and its geometrical meaning
Vignolo Stefano;Fabbri Luca
2025-01-01
Abstract
In this paper, we present geometrical interpretations of the Lie derivative and the Lie-invariance for an affine connection, based on two geometrical constructions: the former is given on the tangent bundle and relies on the notion of linear Ehresmann connection; the latter is developed on the frame bundle and is based on the more common notion of principal connection.
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