Induced connections on manifolds in spaces with fundamental groups (Q2501644)

Varieties with degenerate Gauss maps are multidimensional analogues of developable surfaces in three-dimensional Euclidean space. In this paper, a relation is established between the theory of such varieties in projective space and the theory of congruences of subspaces of a projective space. These two theories are applied to the construction of induced connections on submanifolds of a projective space. Structure equations and curvature tensors are studied. The projective space in addition may carry an affine or Euclidean structure. Further topics are focal points of a variety with degenerate Gauss map and of a congruence of subspaces. As another example we mention the following result: The induced affine connection and the normal connection of a centrally normalized variety are flat.