About geometrical objects fields of the -framed hypersurface of the projective space
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 ...
Fundamental-group connections, induced by composite clothing of family of centered planes in projective space
This paper continues the cycle of works dealing with connections on a smooth family of centered planes in projective space. It is shown that composite clothing of such a family induces three-parameter bunch of bundles of fundamental-group connections. One induced connection is allocated from each of this bundles. Coincidence conditions of the received connections and geometrical interpretation of the linear sub connections is given.
1. Белова О. О. Геометрическая ...
Covariant differentials and covariant derivatives associated with surface of projective space
The paper is concerned with m-dimensional surface in n-dimensional projective space. In studying fundamental-group connection Bianchi identities are found. It is proved that alternated covariant derivatives for the components of the first type connection object are equal to the corresponding components of the curvature tensor, and the ones of the third type vanish....
The curvature object of the fundamental-group connection of the second-order
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.
1. Лаптев Г. Ф. Дифференциальная геометрия погруженных многообразий. Теоретико-групповой метод...