2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75809The topological condition for the existence of a $pin^c$ structure on the product of two Riemannian manifolds is derived and applied to construct examples of manifolds having the weaker Lipschitz structure, but no $pin^c$ structure. An example of a five-dimensional manifold with this property is given; it is pointed out that there are no manifolds of lower dimension with this property.10 pagesDifferential GeometryMathematical Physics53C27,57R15text