scholarly journals Some relations in non-symmetric affine connection spaces with regard to a special almost geodesic mappings of the third type

Filomat ◽  
2015 ◽  
Vol 29 (9) ◽  
pp. 1941-1951 ◽  
Author(s):  
Mica Stankovic ◽  
Nenad Vesic
Keyword(s):  
Affine Connection ◽  
The Third ◽  
Curvature Tensors

We investigate two kinds of special almost geodesic mappings of the third type in this paper. We also find some relations for curvature tensors of almost geodesic mappings of the third type.

About differential equations of the curvature tensors of a fundamental group and affine connections

2019 ◽  
pp. 133-140
Author(s):  
N. Ryazanov
Keyword(s):  
Differential Equations ◽  
Fundamental Group ◽  
Curvature Tensor ◽  
Principal Bundle ◽  
Group Structure ◽  
Affine Connection ◽  
Affine Connections ◽  
First Order ◽  
Structure Equations ◽  
Curvature Tensors

The principal bundle is considered, the base of which is an n-dimensional smooth manifold, and the typical fiber is an r-fold Lie group. Structure equations for the forms of the fundamental group and affine connections are given, each of which contains the corresponding components of the curvature tensor. For each connection, an approach is shown that allows to find the differential equations for the components of the curvature tensor of the corresponding connection in a faster way than by differentiating the expressions of these objects in terms of the connection objects and their Pfaffian derivatives. The method consists in successively solving cubic equations, first by Laptev’s lemma, then by Cartan’s lemma. Taking into account the comparisons modulo basic forms, we obtain already known results (see [3]). Thus, differential equations are derived for the components of the curvature tensor of the first-order fundamentalgroup connection, as well as for the components of the curvature tensor of the affine connection.

scholarly journals Generalized Affine Connections Associated with the Space of Centered Planes

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 782
Author(s):  
Olga Belova
Keyword(s):  
Projective Space ◽  
Affine Connection ◽  
Affine Connections ◽  
Curvature Tensors

Our purpose is to study a space Π of centered m-planes in n-projective space. Generalized fiberings (with semi-gluing) are investigated. Planar and normal affine connections associated with the space Π are set in the generalized fiberings. Fields of these affine connection objects define torsion and curvature tensors. The canonical cases of planar and normal generalized affine connections are considered.

scholarly journals Some properties of ET-projective tensors obtained from Weyl projective tensor

Filomat ◽  
2015 ◽  
Vol 29 (3) ◽  
pp. 573-584
Author(s):  
Mica Stankovic ◽  
Milan Zlatanovic ◽  
Nenad Vesic
Keyword(s):  
Curvature Tensor ◽  
Affine Connection ◽  
Connection Coefficients ◽  
Linearly Independent ◽  
Projective Curvature ◽  
Projective Tensor ◽  
Connection Space ◽  
Curvature Tensors

Vanishing of linearly independent curvature tensors of a non-symmetric affine connection space as functions of vanished curvature tensor of the associated space of this one are analyzed in the first part of this paper. Projective curvature tensors of a non-symmetric affine connection space are expressed as functions of the affine connection coefficients and Weyl projective tensor of the corresponding associated affine connection space in the second part of this paper.

Fields of geometric objects associated with compiled hyperplane-distribution in affine space

2020 ◽  
pp. 103-115
Author(s):  
Yu. I. Popov
Keyword(s):  
Projective Space ◽  
Tangent Bundle ◽  
Affine Space ◽  
Affine Connection ◽  
Distribution Characteristic ◽  
Normal Bundles ◽  
Geometric Objects ◽  
Dimensional Projective Space ◽  
Curvature Tensors ◽  
Torsion Free

A compiled hyperplane distribution is considered in an n-dimensional projective space . We will briefly call it a -distribution. Note that the plane L(A) is the distribution characteristic obtained by displacement in the center belonging to the L-subbundle. The following results were obtained: a) The existence theorem is proved: -distribution exists with arbitrary (3n – 5) functions of n arguments. b) A focal manifold is constructed in the normal plane of the 1st kind of L-subbundle. It was obtained by shifting the cen­ter A along the curves belonging to the L-distribution. A focal manifold is also given, which is an analog of the Koenigs plane for the distribution pair (L, L). c) It is shown that a framed -distribution in the 1st kind normal field of H-distribution induces tangent and normal bundles. d) Six connection theorems induced by a framed -distri­bu­tion in these bundles are proved. In each of the bundles , the framed -distribution induces an intrin­sic torsion-free affine connection in the tangent bundle and a centro-affine connection in the corresponding normal bundle. e) In each of the bundles (d) in the differential neighborhood of the 2nd order, the covers of 2-forms of curvature and curvature tensors of the corresponding connections are constructed.

scholarly journals On Ricci type identities in manifolds with non-symmetric affine connection

2013 ◽  
Vol 94 (108) ◽  
pp. 205-217 ◽  
Author(s):  
Svetislav Mincic
Keyword(s):  
Affine Connection ◽  
Curvature Tensors

In [18], using polylinear mappings, we obtained several curvature tensors in the space LN with non-symmetric affine connection ?. By the same method, we here examine Ricci type identities.

Progress report on 21-cm observations at low latitude between longitudes (l 11) 0° and 66°

1967 ◽  
Vol 31 ◽  
pp. 177-179
Author(s):  
W. W. Shane
Keyword(s):  
Preliminary Report ◽  
Progress Report ◽  
Galactic Centre ◽  
Low Latitude ◽  
The Third ◽  
Introductory Lecture ◽  
Centre Region

In the course of several 21-cm observing programmes being carried out by the Leiden Observatory with the 25-meter telescope at Dwingeloo, a fairly complete, though inhomogeneous, survey of the regionl11= 0° to 66° at low galactic latitudes is becoming available. The essential data on this survey are presented in Table 1. Oort (1967) has given a preliminary report on the first and third investigations. The third is discussed briefly by Kerr in his introductory lecture on the galactic centre region (Paper 42). Burton (1966) has published provisional results of the fifth investigation, and I have discussed the sixth in Paper 19. All of the observations listed in the table have been completed, but we plan to extend investigation 3 to a much finer grid of positions.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

Monte Carlo Algorithms for Moments of Transition Arrays

1988 ◽  
Vol 102 ◽  
pp. 79-81
Author(s):  
A. Goldberg ◽  
S.D. Bloom
Keyword(s):  
Monte Carlo ◽  
State Vector ◽  
Basis Vector ◽  
Collective State ◽  
Dispersion Characteristics ◽  
Dipole Strength ◽  
The Third ◽  
Monte Carlo Algorithms ◽  
Third Moment ◽  
Very High

AbstractClosed expressions for the first, second, and (in some cases) the third moment of atomic transition arrays now exist. Recently a method has been developed for getting to very high moments (up to the 12th and beyond) in cases where a “collective” state-vector (i.e. a state-vector containing the entire electric dipole strength) can be created from each eigenstate in the parent configuration. Both of these approaches give exact results. Herein we describe astatistical(or Monte Carlo) approach which requires onlyonerepresentative state-vector |RV> for the entire parent manifold to get estimates of transition moments of high order. The representation is achieved through the random amplitudes associated with each basis vector making up |RV>. This also gives rise to the dispersion characterizing the method, which has been applied to a system (in the M shell) with≈250,000 lines where we have calculated up to the 5th moment. It turns out that the dispersion in the moments decreases with the size of the manifold, making its application to very big systems statistically advantageous. A discussion of the method and these dispersion characteristics will be presented.

Probe size and 5th-order aberration

1987 ◽  
Vol 45 ◽  
pp. 134-135 ◽  
Author(s):  
Zhifeng Shao
Keyword(s):  
Electron Probe ◽  
Spherical Aberration ◽  
Wave Length ◽  
Cylindrical Symmetry ◽  
Electron Wave ◽  
Third Order ◽  
The Third ◽  
Probe Radius ◽  
Small Probe ◽  
Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

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