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
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 ...
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 ...
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.
Связность в расслоении, ассоциированном ...
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 ...
Semiholonomical, holonomical and trivial spaces of affine connection
... Laptev’s lemma semiholonomical, holonomical and trivial manifolds are defined. The Ricci’s identities allowed us to prove semiholonomicity of the space An,n. This semiholonomicity preserves in the space without torsion A’n,n and in the space without curvature ‘An,n , besides the locally affine space Ά’n,n is trivial. Tensor of non-holonomicity of the space An,n is introduced. Vanishing of this tensor makes the space holonomic, H n n A . Also curvature tensor of associated space of affine connection ...
Algorithms for detecting high-gradient areas of the great oceans has increased biological productivity
... the application of remote sensing data to choose areas of the great oceans with increased biological productivity is considered. Submitted algorithm allows sharing this areas in accordance with the data of fisheries statistics. The method of minimum curvature in tension for the solution of problems of gridding data to required grid is considered.
1. Захаров Л. А. Введение в промысловую океанологию : учеб. пособие. Ка-
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 ...
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...
An impacton solution for the vortex filament
... dynamics of vortex filaments is described. The new method is based on application of a binary Darboux transformation to the solutions of the nonlinear Schrödinger equation. A new type of solutions is constructed: the impacton. The explicit form of the curvature and torsion of corresponding vortex filament are calculated.
1. Валландер С. В. Лекции по гидроаэромеханике. Л., 1978.
2. Голованов Н. Н. Геометрическое моделирование....
Mathematical Model of Intramolecular Tautomeric Transformation and the Processes of a Relaxation of the Proton
... transformation is offered, accounts for the vibration of a proton as a result of its interaction with the surrounding medium simulated by the quantized field of radiation. Effective adiabatic potentials of the proton are approximated by the parabolas of various curvatures. The estimation for the vibrational relaxation time and the formula for the constant of tautomeric equilibrium.
Грибов Л. А., Дементьев В. А., Завалий М. В. и др.
Компьютерное моделирование ...
1+1-Dimensional Yang — Mills Equations and Mass via Quasiclassical Correction to Action
... Schrödinger Operators with the Finite-Band Spectrum and the N-soliton Solutions of the Korteweg — de Vries Equation // Teor. Math. Phys. 1975. Vol. 23. P. 51—68.
20. Leble S., Terent'ev I. Model of Elementary Particles Theory in 6-Dimensional Space with Curvature // Theor. Math. Phys. 1973. Vol. 16. P. 291—302.
Leble S. B.
Yang — Mills equations, nonlinear plane wave, Green function diagonal