Riccati PDEs That Imply Curvature-Flatness

In this paper the following three goals are addressed. The first goal is to study some strong partial differential equations (PDEs) that imply curvature-flatness, in cases of both symmetric and non-symmetric connection. Although curvature-flatness idea classic for connection, our main theorems about flatness solutions completely new, leaving a while point view geometry entering PDEs. second introduce relations associated curvature-flatness. third analyze vector spaces exotic objects change meaning generalized Kronecker delta projection operator, order discover new PDEs implying Significant examples clarify ideas.