Geometry of nonholonomic hypercomplexes of multidimensional affine space. II (Q917045)

The properties of the nonholonomic complex \(\mathrm{NGr}(1,n,2n-3)\) in the affine space \(A_n\) are studied. Let the \(3\)-plane \(N_3(\ell)\) intersect the \((n-2)\)-plane \(\Pi_{n-2}\) in the generator \(\ell\) of \(\mathrm{NGr}(1,n,2n-3)\). Let the \((n-4)\)-plane \(N_{n-4}(\ell)\) belong to \(\Pi_{n-2}\) and not pass through \(\ell\). \(N_3(\ell)\), \(N_{n-4}(\ell)\) are called the normals of \(\mathrm{NGr}(1,n,2n-3)\) and \(\mathrm{NGr}(1,n,2n-3)\) is normalized through these planes. The intrinsic normalizations of \(\mathrm{NGr}(1,n,2n-3)\) are studied. The correspondences between the spaces \(N_3(\ell)\) and \(N_{n-4}(\ell)\) of these normalizations are found. The normalizations of E. Cartan and E. Bortolotti of \(\mathrm{NGr}(1,n,2n-3)\) are introduced. The hypercomplex \(\mathrm{NGr}(1,3,3)\) is studied which is the section of \(\mathrm{NGr}(1,n,2n-3)\) through \(N_3(\ell)\). The properties of such \(\mathrm{NGr}(1,n,2n-3)\) which degenerates to the system of holonomic hypercomplexes \(\mathrm{Gr}(1,n,2n-3)\) are found. [Part I, cf. Lith. Math. J. 28, No. 3, 248--259 (1988); translation from Litov. Mat. Sb. 28, No. 3, 534--547 (1988; Zbl 0653.53011).]