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In differential geometry, the Kosmann lift, named after Yvette Kosmann-Schwarzbach, of a vector field X {\displaystyle X\,} on a Riemannian manifold {\displaystyle \,} is the canonical projection X K {\displaystyle X_{K}\,} on the orthonormal frame bundle of its natural lift X ^ {\displaystyle {\hat {X}}\,} defined on the bundle of linear frames.
Generalisations exist for any given reductive G-structure.
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