\(p\)-geodesic transformations induced by infinitesimal holomorphically projective transformations of Kähler spaces
A curve \({\mathcal C}\) in an affinely connected space \((M,\nabla)\) is called an \(m\)-geodesic if it has \(m\)-th order flattening at each of its point, i.e., the first \(m\) covariant derivatives of its tangent vector are linearly independent in every point. A diffeomorphism between two affinely connected spaces is called \(r\)-geodesic if it sends all geodesics of the first space into curves whose points have flattening order no greater than \(r\). The author studies the flattening properties of the infinitesimal transformations of the ( first and second order) tangent bundles of a Kähler manifold, generated by (vertical or complete) lifts of vector fields associated to infinitesimal holomorphically projective transformations.
\(p\)-geodesic infinitesimal transformation
infinitesimal holomorphically projective transformations
scientific article; zbMATH DE number 6148263