Connection in a tangent bundle to the frame bundle of manifold
This 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 геометрии. М., 1981. Т. 1.
3. Лаптев ...
Giving the 1st order affine connection by means of the 2nd order vector-valued forms
... connection in the bundle of tangent linear frames defines vertical linear operator (a vertical vertical-valued form of 2nd order for 1st order affine connection) from 2nd order tangent space into 1st order tangent space to a manifold. It is shown that affine connection in bundle of tangent lin-ear frames defines linear operator from 1st order cotangent space (space of forms of degree 1) in cotangent space of 2nd order. It is proved that affine connection in bundle of tangent linear frames defines horizontal linear operator (2nd ...
Fundamental-group connections, induced by composite clothing of family of centered planes in projective space
... многообр. фигур. Вып. 9. Калининград, 1978. С. 124—133.
12. Cartan E. Lecons sur la theorie des espaces a connexion projective. P., 1937.
projective space, family of centered planes, fundamental-group connection, bundle of connections, composite equipment, central projection, Cartan — Laptev’s method.
Eliseeva N. A., Popov Y. I.
... authors construct Foss and Green's normalizations in Norden's sense internally invariantly. The research sets tangent affine connections and tangent central affine connections of the main structural subbundles of H(L, L)-distribution of affine space.
1. Попов Ю. И. Нормализация ... ... М., 1973. Т. 4. С. 7—70.
On constructions in Н(Λ, L)-distribution geometry of affin space
tensor, quasitensor, subbundle, bundle, linear polar, Bompiani—Pantazi correspondence, distribution, normalization, affine connection, central affine ...
The derivation formulas and equations for an affine space structure from the point of view of smooth manifolds
... geometry of special mappings. Olomouc, 2015.
13. Shevchenko Ju. I., Skrydlova E. V. About non-holonomicity of quotient manifold of holonomic distribution on semi-holonomic smooth manifold // Междун. конф. по алгебре, анализу и ... ...
Akivis derivation formulas, Laptev structure equations, secondorder vectors, semi-holonomic smooth manifold, bundle or linear coframes, affine connection
Introduction of connections on a hypersurface ()
... 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
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 are made. These comparisons show that the curvature object forms a geometric ...
Hierarchies of smooth manifolds up to zeroth and first orders
Hierarchies of smooth manifolds in the form of sequences are given. The sequence of zero order consists of the parallelized manifold, Lie ... ... 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 ...
About generalizations of the Cartan projective connection on smooth manifold
... 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.
1. Лаптев Г. Ф. Основные инфинитезимальные структуры высших ...
Normal connections of the L-subbundle of a strongly mutual distribution of the projective space
... 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 bundles of the 1st and 2nd kind normals of the L-subbundle of this VH -distribution are examined.
1. Попов Ю. И. Сильно взаимные трехсоставные распределения проективного пространства // ...