Differentiable Mappings of Affine Spaces into Manifolds of in-Planesin a Multidimensional Euclidean Space

摘要

In this paper we consider a differentiable mapping of a p-dimensional affine space intothe differentiable manifold m_N of all centered m-planes in an n-dimensional Euclidean space. Wepay special attention to describing geometric images defined by a fundamental geometric object ofthe mentioned mapping.