Kosmann lift

In differential geometry, the Kosmann lift, named after Yvette Kosmann-Schwarzbach, of a vector field ${\displaystyle X\,}$ on a Riemannian manifold ${\displaystyle (M,g)\,}$ is the canonical projection ${\displaystyle X_{K}\,}$ on the orthonormal frame bundle of its natural lift ${\displaystyle {\hat {X}}\,}$ defined on the bundle of linear frames.

Generalisations exist for any given reductive G-structure.