2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67964We obtain bounds on the least dimension of an affine space that can contain an $n$-dimensional submanifold without any pairs of parallel or intersecting tangent lines at distinct points. This problem is closely related to the generalized vector field problem, non-singular bilinear maps, and the immersion problem for real projective spaces.Differential Geometrytext