Differential geometry of $(n-m)m$-dimensional complexes in $n$-dimensional projective space

We consider an $(n-m)m$-dimensional complex in the projective space $P_n$. In the principal bundle associated with this complex, we construct a fundamental-group connection and calculate the curvature and torsion of this connection. We examine this complex by the Cartan–Laptev method. We prove that the fundamental object of the $1$th order of this complex is a pseudoquasitensor, the curvature is a pseudotensor, and the torsion is a geometric object only in combination with the connection subobject and the fundamental object. We perform the compositional framing of the $(n-m)m$-dimensional complex. Also, we prove that this framing induces connections of three types in the principal bundle associated with the complex.