2014 Issue №10

Norden inner normalization fields of basic structural subbundle of hyperband distribution are constructed in second order differential neighborhood of affine space. It is showed that first order normal (L-virual affine normal, Blashke normal, Trenson normal) corresponding to each of subbundle belongs to the same sheaf in any center A. Sheafs of second order normal of Λ-, L-, H-subbundle correspond to them in the Bompiani–Pantazi bijection. Analytical coincidence features of H -distribution and its Λ-, L-, H-subbundle was clarified.

The Laptev projective structure of the 1st order presented a fibering of special linear coframes with multidimensional gluing is considered. The Laptev linear connection by means of the object containing a tensor is set in this fibering. If the tensor vanishes we have preprojective connection from which canonical connection is marked out. The Cartan projective connection and its canonical version are obtained from a projectivity condition. On the other hand, the projective structure is presented in the form of the principal fiber bundle of the special center-linear coframes. The giving fundamental- group connection in this fibering is made by means of the center-linear connection object, not coinciding with the previous objects of connections.

A subclass of three-parametrical collection of ellipsoids in three-dimensional affine space is investigated. The construction of the considered manifold is given.

In many-dimensional projective space the plane distribution is considered. The curvature of group connection of 2-nd type, induced by composite clothing of plane distribution, is constructed. It is proved, that a immovability of Cartan’s plane and Bortolotti’s hyperplane in case of holonomic distribution attracts the vanishing of curvature tensor of 2-nd type.