Results: **10**

#### 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 ...

#### Differential comparisons for the components of the **curvature** object of affine connection of the second order

Differential comparisons for the components of the **curvature** object of affine connection of the second order are received. These comparisons show that, in the general case, the second-order **curvature** object forms a geometric object only in conjunction with the first-order **curvature** object and the second-order ...

#### Introduction of connections on a hypersurface ()

The paper introduces internal affine (tangent) and normal (centroprojective) connections on normalized (Norden’s framed) hypersurface n-1() Pn in its various subbundles. Coverages of the corresponding **curvature** 2 forms and **curvature** tensors of its connections are given.
Popov Yu. I.
normalization, bundle, subbundle, affine connection, centrorojective connection (normal connection), **curvature** 2 form, **curvature** tensors of connection
18-24

**Curvature** of 2nd type induced on plane distribution

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 ...

#### Representation of projective connections on the SH -distribution of the projective space

Projective connections defined by projection and associated to subbundles , L, E of the strong dual threefold distribution (the SH -distribution) of the projective space are constructed. Coverages of torsion-curvature tensors components of the constructed projective connections , , of subbundles , L, E of the SH -distribution respectively are given. The way of creation of dual projective connections , , corresponding to connections , , is specified. 1. Попов...

#### Connection in a tangent bundle to the frame bundle of manifold

... paper focuses on the tangent bundle to the linear frame bundle of a smooth manifold. Brackets of the tangent vectors of this bundle are con-structed. A coordinate representation of the non-holonomic frame vectors is produced. Horizontal and vertical **curvatures**, torsions, and covariant derivatives are constructed in a homogeneous connection.
Бишоп Р., Криттенден Р. Геометрия многообразий. М., 1967.
2. Кобаяси Ш., Номидзу К. Основы дифференциальной ...

#### Covariant differentials and covariant derivatives associated with surface of projective space

... 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.
1. Шевченко Ю. И. Об основной задаче проективно-дифференциальной геометрии поверхности // Диф. геом. многообр....

#### Normal generalized affine connection associated with the Grassman-like manifold of centred planes

In projective space a Grassman-like manifold of centred planes is considered. The normal affine connection, associated with the manifold, is set in generalized fibering. Field of the affine connection object defines torsion and **curvature** tensors contained one elementary and one simple subtensor every. A canonical case of normal generalized affine connection is considered.
1.
Белова
О. О.
Связность в расслоении, ассоциированном ...

#### A semicanonical normal affine connection associated with the distribution

... distribution of planes is considered. The way of giving normal generalized affine connection associated with the distribution is proposed. It is shown that this connection is given by connection tensor and normal linear connection object. They define its **curvature** and torsion tensors. Semicanonical case is investigated when subtensor of the connection tensor vanishes. Two notions are
involved: non-degeneration tensor of torsion and semiholonomical distribution. It is proved that vanishing of non-degeneration ...

#### Normal connections of the L-subbundle of a strongly mutual distribution of the projective space

The special class of the threefold distributions of the projective space Pn — VH -distribution — is considered. In each center X of VH -distribution the incidence relation of the elements of the -, M-, H-subbundle has an appearance X r Mm Hn1, where r m n 1. This class is characterized by the fact that the pairs (, ), (L, ), (M, E) of the main structural subbundles of this threefold distribution are mutual. Invariant dual normal connections induced in...