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