Complete k-curvature homogeneous pseudo-Riemannian manifolds

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71039For any k which is at least 2, we exhibit complete k-curvature homogeneous neutral signature pseudo-Riemannian manifolds which are not k+1-affine curvature homogeneous, and hence not locally homogeneous. All the local scalar Weyl invariants of these manifolds vanish. These manifolds are Ricci flat, Osserman, and Ivanov-Petrova.Differential Geometry53B20Complete k-curvature homogeneous pseudo-Riemannian manifoldstext