scholarly journals On a structure satisfyingFK−(−)K+1F=0

1996 ◽  
Vol 19 (1) ◽  
pp. 125-130 ◽  
Author(s):  
Lovejoy S. Das
Keyword(s):  
Tensor Field ◽  
Differentiable Manifold

In this paper we shall obtain certain results on the structure defined byF(K,−(−)K+1)and satisfyingFK−(−)K+1F=0, whereFis a non null tensor field of the type(1,1)Such a structure on ann-dimensional differentiable manifoldMnhas been calledF(K,−(−)K+1)structure of rank “r”, where the rank ofFis constant onMnand is equal to “r” In this caseMnis called anF(K,−(−)K+1)manifold. The case whenKis odd has been considered in this paper

scholarly journals A theorem on polynomial lorentz structures

1986 ◽  
Vol 28 (2) ◽  
pp. 229-235
Author(s):  
Krzysztof Deszyński
Keyword(s):  
Tensor Field ◽  
Vector Fields ◽  
Minimal Polynomial ◽  
Differentiable Manifold ◽  
Real Numbers ◽  
Lorentz Structure ◽  
Polynomial Structure ◽  
Image Position

Let M be a differentiable manifold of dimension m. A tensor field f of type (1, 1) on M is called a polynomial structure on M if it satisfies the equation:where a1, a2, …, an are real numbers and I denotes the identity tensor of type (1, 1).We shall suppose that for any x ∈ Mis the minimal polynomial of the endomorphism fx: TxM → TxM.We shall call the triple (M, f, g) a polynomial Lorentz structure if f is a polynomial structure on M, g is a symmetric and nondegenerate tensor field of type (0, 2) of signaturesuch that g (fX, fY) = g(X, Y) for any vector fields X, Y tangent to M. The tensor field g is a (generalized) Lorentz metric.

Selfadjoint Metrics on Almost Tangent Manifolds Whose Riemannian Connection is Almost Tangent

1975 ◽  
Vol 17 (5) ◽  
pp. 671-674
Author(s):  
D. S. Goel
Keyword(s):  
Tensor Field ◽  
Complex Structure ◽  
Differentiable Manifold ◽  
Riemannian Metric ◽  
Almost Complex Structure ◽  
Constant Rank ◽  
Real Constant ◽  
Almost Complex ◽  
Riemannian Connection ◽  
Almost Tangent Structure

Let M be a differentiable manifold of class C∞, with a given (1, 1) tensor field J of constant rank such that J2=λI (for some real constant λ). J defines a class of conjugate (G-structures on M. For λ>0, one particular representative structure is an almost product structure. Almost complex structure arises when λ<0. If the rank of J is maximum and λ=0, then we obtain an almost tangent structure. In the last two cases the dimension of the manifold is necessarily even. A Riemannian metric S on M is said to be related if one of the conjugate structures defined by S has a common subordinate structure with the G-structure defined by S. It is said to be J-metric if the orthogonal structure defined by S has a common subordinate structure.

scholarly journals Spherically Symmetric Tensor Fields and Their Application in Nonlinear Theory of Dislocations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 830
Author(s):  
Evgeniya V. Goloveshkina ◽  
Leonid M. Zubov
Keyword(s):  
Nonlinear Theory ◽  
Hollow Sphere ◽  
Tensor Field ◽  
Exact Analytical Solution ◽  
Symmetric Tensor ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Tensor Fields ◽  
Spherically Symmetric Distribution ◽  
Nonlinear Elastic

The concept of a spherically symmetric second-rank tensor field is formulated. A general representation of such a tensor field is derived. Results related to tensor analysis of spherically symmetric fields and their geometric properties are presented. Using these results, a formulation of the spherically symmetric problem of the nonlinear theory of dislocations is given. For an isotropic nonlinear elastic material with an arbitrary spherically symmetric distribution of dislocations, this problem is reduced to a nonlinear boundary value problem for a system of ordinary differential equations. In the case of an incompressible isotropic material and a spherically symmetric distribution of screw dislocations in the radial direction, an exact analytical solution is found for the equilibrium of a hollow sphere loaded from the outside and from the inside by hydrostatic pressures. This solution is suitable for any models of an isotropic incompressible body, i. e., universal in the specified class of materials. Based on the obtained solution, numerical calculations on the effect of dislocations on the stress state of an elastic hollow sphere at large deformations are carried out.

scholarly journals Erratum to: Hints of unitarity at large N in the O(N)3 tensor field theory

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Dario Benedetti ◽  
Razvan Gurau ◽  
Sabine Harribey ◽  
Kenta Suzuki
Keyword(s):  
Field Theory ◽  
Tensor Field ◽  
Normalization Factor ◽  
Large N

The measure in equation (2.11) contains a wrong normalization factor, and it should be multiplied by 21−dΓ(d − 1)/Γ(d/2)2.

A survey on visualization of tensor field

2019 ◽  
Vol 22 (3) ◽  
pp. 641-660 ◽  
Author(s):  
Chongke Bi ◽  
Lu Yang ◽  
Yulin Duan ◽  
Yun Shi
Keyword(s):  
Tensor Field

SINGULAR SWITCHED LINEAR SYSTEMS: SOME GEOMETRIC ASPECTS

2012 ◽  
Vol 26 (25) ◽  
pp. 1246006
Author(s):  
H. DIEZ-MACHÍO ◽  
J. CLOTET ◽  
M. I. GARCÍA-PLANAS ◽  
M. D. MAGRET ◽  
M. E. MONTORO
Keyword(s):  
Linear Systems ◽  
Group Action ◽  
Lie Group ◽  
Equivalence Relation ◽  
Geometric Approach ◽  
Differentiable Manifold ◽  
Equivalence Classes ◽  
Switched Linear Systems ◽  
Lie Group Action

We present a geometric approach to the study of singular switched linear systems, defining a Lie group action on the differentiable manifold consisting of the matrices defining their subsystems with orbits coinciding with equivalence classes under an equivalence relation which preserves reachability and derive miniversal (orthogonal) deformations of the system. We relate this with some new results on reachability of such systems.

scholarly journals Invariant connections and invariant holomorphic bundles on homogeneous manifolds

2014 ◽  
Vol 12 (1) ◽  
pp. 1-13
Author(s):  
Indranil Biswas ◽  
Andrei Teleman
Keyword(s):  
Lie Group ◽  
Complex Structure ◽  
Differentiable Manifold ◽  
Equivalence Classes ◽  
Transitive Action ◽  
Isomorphism Classes ◽  
Finite Dimensional ◽  
Group A ◽  
Holomorphic Bundles ◽  
Invariant Gauge

AbstractLet X be a differentiable manifold endowed with a transitive action α: A×X→X of a Lie group A. Let K be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms of explicit finite dimensional quotients, of three classes of objects:equivalence classes of α-invariant K-connections on X α-invariant gauge classes of K-connections on X, andα-invariant isomorphism classes of pairs (Q,P) consisting of a holomorphic Kℂ-bundle Q → X and a K-reduction P of Q (when X has an α-invariant complex structure).

Can a tensorial analogue of gravitational force explain away the galactic rotation curves without dark matter?

2021 ◽  
Author(s):  
Ram Gopal Vishwakarma
Keyword(s):  
Dark Matter ◽  
Tensor Field ◽  
Gravitational Force ◽  
Direct Detection ◽  
Alternative Theory ◽  
Galactic Rotation ◽  
Rotation Curves ◽  
Modern Physics ◽  
Flat Rotation Curves ◽  
Relativistic Analogue

The dark matter problem is one of the most pressing problems in modern physics. As there is no well-established claim from a direct detection experiment supporting the existence of the illusive dark matter that has been postulated to explain the flat rotation curves of galaxies, and since the whole issue of an alternative theory of gravity remains controversial, it may be worth to reconsider the familiar ground of general relativity (GR) itself for a possible way out. It has recently been discovered that a skew-symmetric rank-three tensor field — the Lanczos tensor field — that generates the Weyl tensor differentially, provides a proper relativistic analogue of the Newtonian gravitational force. By taking account of its conformal invariance, the Lanczos tensor leads to a modified acceleration law which can explain, within the framework of GR itself, the flat rotation curves of galaxies without the need for any dark matter whatsoever.

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