A semicanonical normal affine connection associated with the distribution
In manydimensional projective space 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 ...
Giving the 1st order affine connection by means of the 2nd order vector-valued forms
Affine connection is given by 2nd order vectors called horizontal. Vertical and horizontal forms of 2nd order are entered for 1st order affine connection. It is proved that symmetric affine connection in the bundle of tangent linear frames defines vertical linear ...
About generalizations of the Cartan projective connection on smooth manifold
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 ...
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 ...
Semiholonomical, holonomical and trivial spaces of affine connection
In n-dimensional space of affine connection An,n with Cartan’s structure equations Ricci’s and Bianchi’s identities were received. Their invariance has been shown. After prolongation of the structure equations using Laptev’s lemma semiholonomical, holonomical and trivial manifolds ...
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 ...
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,...
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 connectivity object....
Hierarchies of smooth manifolds up to zeroth and first orders
... and Abelian group of Lie. Each of three sequences of the 1st order for the ho-lonomic, semi-holonomic and the non- holonomic smooth manifolds includes base of the parallelized bundle of linear coframes, in other words, base of space of expanded affine connection, base of space of affine connection torsion-free and affine space.
1. Лаптев Г. Ф. Основные инфинитезимальные структуры высших поряд-ков на гладком многообразии ...
The torsion tensor of an analog of the Neifeld connection on a Grass-mannian-like manifold of centered planes
... Калининград, 2014. № 45. С. 23—29.
5. Шевченко Ю. И. Оснащения центропроективных многообразий. Калинин¬град, 2000.
Belova O.
projective space, Grassmannian-like manifold, connection, Neifeld connection, torsion tensor.
103-105
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....
List of lexical combinations in the macrostructure of a frequency author dictionary: on forwarding the problem
... discovered in different poems, forming the implicit composition of the analyzed poetic corpus. The applied significance of lexical combinations in the focus of authorial lexicography is determined: the obtained information about hidden intertextual connections refines the role of keywords and complements the dictionary’s card file, opening up broad prospects for a multi-dimensional analysis of Boris Ryzhy’s lexical heritage.
Baranovskii P.S.
lexical combinations, intertextual connections,...