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 of the connection tensor vanishes. Two notions are
involved: non-degeneration tensor of torsion and semiholonomical ...
Pseudovector and its parallel displacement
Covariant derivatives of tangent tensor and pseudotensor are considered. Parallel displacements of tangent tensor and pseudotensor are described.
1. Абрамов А. . Введение в тензорный анализ и риманову геометрию. M., 2012.
2. Акивис ...
About horizontally vector lifts of tensor fields from the base to its tangent bundle
The vector field of the type , obtained fr om the tensor field on a smooth manifold M to the tangent bundle , arises in the study of infinitesimal affine transformations with a complete lift. The H-lift was introduced S. Tanno in 1974 in infinitesimal isometries on the tangent bundle with the complete ...
The torsion tensor of an analog of the Neifeld connection on a Grass-mannian-like manifold of centered planes
This article considers the Grassmanian-like manifold of cen-tered m-planes in the projective space Pn. A torsion object of the Neifeld con-nection is introduced in the fibering over the manifold . It is shown that this object forms a tensor containing one elementary and four simple subtensors.
1. Белова О. О. Связность в расслоении, ассоциированном с грассманоподобным многообразием центрированных ...
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
... 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.
1. Лаптев Г. Ф., Остиану Н. М. Распределения m-мерных линейных элементов в пространстве проективной связности I // Тр. геом. семинара ...
Strongly mutual threefold distributions of projective space
... Т.7. С. 117 151.
5. Лаптев Г. Ф. Дифференциальная геометрия погруженных многообразий. // Тр. моск. мат. об-ва. 1953. Т.2. С. 275 382.
Popov Yu.
distribution, nonholonomic tensor, holonomic distribution, hyperband, tensor, quasitensor, duality of distribution, adjoint surface system, quasinormal, subbundle.
62-67
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 с грассманоподобным ...
Eliseeva N. A., Popov Y. I.
... Швейкин П. И. Очерк научных исследований Германа Федоровича Лаптева // Тр. геом. семинара. 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 connection
5-17
Normalization of the basic structural subbundles of the H(, L)-distribution of affine space
... федерального университета им. И. Канта. 2013. Вып. 10 : Физико-математические науки. С. 49—56.
Popov Y. I.
Bompiani — Pantazi correspondence, normalization, distribution, subbundle, tensor, quasitensor
5-14
Normal connections of the L-subbundle of a strongly mutual distribution of the projective space
... : сб. статей по материалам XXVII международной конференции. Новосибирск, 2015. № 2(26). С. 33—47.
Popov Ju., Volkova S.
distribution, projective connection, subbundle, torsion-curvature tensor, projective connection object, geometrical object, geometrical object coverage
5-17
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 , , ...
Fields of fundamental and captured geometrical objects of the 2nd or-der H-distribution of affine space
Norden inner normalization fields of basic structural Λ-, L-, H-sub-bundle of hyperband H-distribution are constructed in 2nd order differential neighborhood of affine space An by means of symmetric fundamental tensors of 1st order.
1. Попов Ю. И. Введение в теорию регулярного гиперполостного распреде-ления аффинного пространства // Вестник Балтийского федерального ...
Invariant normalizations and É. Cartan equips of main structural subbundles of SH-distribution
... форм Картана. М., 1948.
13. Cartan E. Les espaces a connexion projective // Тр. семинара по векторному и тензорному анализу МГУ. М., 1977. Вып. 4. С. 147—159.
Budylkin A.
distribution, tensor, kvazitensor, normalization
41-50
Strongly associated threefold distributions of projective space
... университет, 1982. Рук. деп. ВИНИТИ 16.12.1982. № 6192-82Деп.
11. Норден А. П. Пространства аффинной связности. М., 1976.
Popov Ju.
distribution, duality of distribution, adjoint surface system, tensor, quasitensor, subbundle, quasinormal
5-18
Normalization of basic structural subbundle of distribution in second order differential neighborhood
... гиперполосного распределения аффинного пространства // Диф. геом. многообр. фигур. Калининград, 1988. Вып. 19. С. 69—79.
Popov Yu.
subbundle, normalization, normal, tensor, quasitensor, distribution, coincidence, bijection
53-59
About fields of geometrical objects connected with the complex central nondegenerate hyperquadrics
... расслоениях многообразий плоскостей // Матем. сб. М., 1973. Т. 91, № 2. С. 211—233.
Kretov M.
complex, hyperquadric, hypercone, manifold, hyperellipsoid, affine space, geometrical object, Pfaff's equation, tensor
76-80
