2017 Issue №4

The second-order curvature object contains the curvature object of the fundamental-group connection defined in the principal bundle; the curvature object of an affine connection over a manifold; second-order components. Differential comparisons for the components of the object of curvature of the second- order fundamental-group connection are made. These comparisons show that the curvature object forms a geometric object only in combination with components of the second-order connectivity object. In the general case, the object of curvature of the fundamental group connection of the second order does not form a tensor.

The special class of (-framed) hypersurfaces of the projective space Pn — is defined, and its existence theorem is proved. In the differential 3rd order neighbourhood: (a) Norden–Timofeyev's normalization of the hypersurface; (b) two Norden's normalizations of the tangent -subbundle; (c) in each L-plane three one-parameter sheaves of its Norden's 2nd kind normals–are constructed internally invariantly.

Non effective, factor-effective and special-effective projective spaces are considered. In an non effective projective space the linear group is acting. When one index value is isolated in the Cartan structure equations of a linear group, the hierarchy of its seven subgroups is constructed.