The proposed single shooting method can be extended to handle more general Riemannian metrics on the Stiefel manifold by incorporating the metric tensor into the geodesic equation. In the context of Riemannian geometry, the geodesic equation is typically defined in terms of the Levi-Civita connection, which is determined by the metric tensor. By modifying the geodesic equation to include the metric tensor, the single shooting method can be adapted to work with different metrics on the Stiefel manifold.