On a Grassmann-like manifold and an analog of the Neufeld connection

The invariant analytic Cartan–Laptev method is applied to the study of a Grassmann-like manifold of centered planes in the projective space. In a principal bundle over this manifold, an analog of the Neufeld connection is constructed. We prove that an analog of the strong Norden normalization induces an analog of the Neufeld connection. The curvature and torsion objects of this connection are analyzed and compared with similar objects for Grassmann manifolds and the space of centered planes.