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1.
We have studied the conformal, homothetic and Killing vectors in the context of teleparallel theory of gravitation for plane-symmetric static spacetimes. We have solved completely the non-linear coupled teleparallel conformal Killing equations. This yields the general form of teleparallel conformal vectors along with the conformal factor for all possible cases of metric functions. We have found four solutions which are divided into one Killing symmetries and three conformal Killing symmetries. One of these teleparalel conformal vectors depends on x only and other is a function of all spacetime coordinates. The three conformal Killing symmetries contain three proper homothetic symmetries where the conformal factor is an arbitrary non-zero constant. 相似文献
2.
L. Defrise-Carter 《Communications in Mathematical Physics》1975,40(3):273-282
It is shown that if ann dimensional Riemannian or pseudo-Riemannian manifold admits a proper conformal scalar, every (local) conformal group is conformally isometric, and that if it admits a proper conformal gradient every (local) conformal group is conformally homothetic. In the Riemannian case there is always a conformal scalar unless the metric is conformally Euclidean. In the case of a Lorentzian 4-manifold it is proved that the only metrics with no conformal scalars (and hence the only ones admitting a (local) conformal group not conformally isometric) are either conformal to the plane wave metric with parallel rays or conformally Minkowskian. 相似文献
3.
Conformal invariance, Noether symmetry, Lie symmetry and conserved quantities of Hamilton systems
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In this paper, the relation of the conformal invariance, the Noether symmetry, and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is given. The relation between the conformal invariance and the Noether symmetry is discussed, the conformal factors of the determining expressions are found by using the Noether symmetry, and the Noether conserved quantity resulted from the conformal invariance is obtained. The relation between the conformal invariance and the Lie symmetry is discussed, the conformal factors are found by using the Lie symmetry, and the Hojman conserved quantity resulted from the conformal invariance of the system is obtained. Two examples are given to illustrate the application of the results. 相似文献
4.
This paper focuses on studying a conformal invariance and a Noether symmetry, a Lie symmetry for a Birkhoffian system in event space. The definitions of the conformal invariance of the system are given. By investigation on the relations between the conformal invariance and the Noether symmetry, the conformal invariance and the Lie symmetry, the expressions of conformal factors of the system under these circumstances are obtained. The Noether conserved quantities and the Hojman conserved quantities directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results. 相似文献
5.
《Optik》2014,125(24):7120-7125
The aerodynamic flow field surrounding the conformal dome was calculated. The thermal response of the aerodynamically heated conformal dome was analyzed. Gradient refractive index method was used to rebuild the non-uniform refractive index field of the conformal dome. Zernike polynomial fitting method was employed to establish the deformed surfaces of the conformal dome. Zernike aberration theory and modulation transfer function were adopted to evaluate the imaging quality of the conformal optical system. The results show that the aerodynamic heating of the dome severely affects the imaging quality of the conformal optical system. 相似文献
6.
Conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems
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This paper studies conformal invariance and conserved
quantity of third-order Lagrange equations for non-conserved
mechanical systems. Third-order Lagrange equations, the definition
and a determining equation of conformal invariance of the system are
presented. The conformal factor expression is deduced from conformal
invariance and Lie symmetry. The necessary and sufficient condition
that conformal invariance of the system would have Lie symmetry under
single-parameter infinitesimal transformations is obtained. The
corresponding conserved quantity of conformal invariance is derived
with the aid of a structure equation. Lastly, an example is given to
illustrate the application of the results. 相似文献
7.
Conformal invariance and conserved quantities of Birkhoff systems under second-class Mei symmetry
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This paper proposes a new concept of the conformal invariance and the conserved quantities for Birkhoff systems under second-class Mei symmetry.The definition about conformal invariance of Birkhoff systems under second-class Mei symmetry is given.The conformal factor in the determining equations is found.The relationship between Birkhoff system’s conformal invariance and second-class Mei symmetry are discussed.The necessary and sufficient conditions of conformal invariance,which are simultaneously of second-class symmetry,are given.And Birkhoff system’s conformal invariance may lead to corresponding Mei conserved quantities,which is deduced directly from the second-class Mei symmetry when the conformal invariance satisfies some conditions.Lastly,an example is provided to illustrate the application of the result. 相似文献
8.
Conformal invariance and generalized Hojman conserved quantities of mechanico-electrical systems
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This paper studies conformal invariance and generalized
Hojman conserved quantities of mechanico-electrical systems. The
definition and the determining equation of conformal invariance for
mechanico-electrical systems are provided. The conformal factor
expression is deduced from conformal invariance and Lie symmetry
under the infinitesimal single-parameter transformation group. The
generalized Hojman conserved quantities from the conformal
invariance of the system are given. An example is given to
illustrate the application of the result. 相似文献
9.
Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space
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This paper is devoted to studying the conformal invariance
and Noether symmetry and Lie symmetry of a holonomic mechanical
system in event space. The definition of the conformal invariance
and the corresponding conformal factors of the holonomic system in
event space are given. By investigating the relation between the
conformal invariance and the Noether symmetry and the Lie symmetry,
expressions of conformal factors of the system under these
circumstances are obtained, and the Noether conserved quantity and
the Hojman conserved quantity directly derived from the conformal
invariance are given. Two examples are given to illustrate the
application of the results. 相似文献
10.
This paper studies the conformal invariance and conserved quantities
of general holonomic systems in phase space. The definition and the
determining equation of conformal invariance for general holonomic
systems in phase space are provided. The conformal factor expression
is deduced from conformal invariance and Lie symmetry. The
relationship between the conformal invariance and the Lie symmetry
is discussed, and the necessary and sufficient condition that the
conformal invariance would be the Lie symmetry of the system under
the infinitesimal single-parameter transformation group is deduced.
The conserved quantities of the system are given. An example is
given to illustrate the application of the result. 相似文献
11.
12.
This work concerns, in part, the construction of conformal Jordan cells of infinite rank and their reductions to conformal
Jordan cells of finite rank. How a procedure similar to Lie algebra contractions may reduce a conformal Jordan cell of finite
rank to one of lower rank is also discussed. A conformal Jordan cell of rank one corresponds to a primary field. This offers
a picture in which any finite conformal Jordan cell of a given conformal weight may be obtained from a universal covering
cell of the same weight but infinite rank.
MSC (2000): 81T40 相似文献
13.
Design of cylindrical conformal transmitted metasurface for orbital angular momentum vortex wave generation
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We propose a cylindrical conformal transmitted metasurface for orbital angular momentum vortex wave generation. Formulas for calculating the phase distributions of cylindrical conformal transmitted metasurface is presented. A prototype of the proposed conformal transmitted metasurface is designed, fabricated and measured. Measured results shows that the proposed conformal transmitted metasurface can effectively generate vortex waves, which verifies the effectiveness of our method. The proposed method may pave the way of vortex wave generation with cylindrical conformal devices. 相似文献
14.
We study the main properties of locally conformal Dirac bundles, which include Dirac structures on a manifold and locally conformal symplectic manifolds. It is proven that certain locally conformal Dirac bundles induce Jacobi structures on quotient manifolds. Furthermore we show that, given a locally conformal Dirac bundle over a smooth manifold M, there is a Lie homomorphism between a subalgebra of the Lie algebra of infinitesimal automorphisms and the Lie algebra of admissible functions. We also show that Dirac manifolds can be obtained from locally conformal Dirac bundles by using an appropriate covering map. Finally, we extend locally conformal Dirac bundles to the context of Lie algebroids. 相似文献
15.
使用新型的特殊整流罩窗口可以明显地提升飞行器的空气动力学性能,但由于这种共形窗口光学表面的复杂性,传统的非球面检测技术已经较难满足要求.本文提出了一种新型子孔径拼接检测技术,在建立新的检测原理基础上,还重点介绍了这种检测方法的设计.同时基于补偿法的原理,文中还针对一个口径70 mm的共形窗口,设计了相应的特殊补偿器,其最终剩余波像差(RMS)为0.0515λ(λ=632.8 nm),可以满足实际使用要求.
关键词:
共形窗口
共形检测
子孔径拼接检测
补偿器 相似文献
16.
We study conformal vector fields on space-times which in addition are compatible with the Ricci tensor (so-called conformal Ricci collineations). In the case of Einstein metrics any conformal vector field is automatically a Ricci collineation as well. For Riemannian manifolds, conformal Ricci collineation were called concircular vector fields and studied in the relationship with the geometry of geodesic circles. Here we obtain a partial classification of space-times carrying proper conformal Ricci collineations. There are examples which are not Einstein metrics. 相似文献
17.
Yi-Ping Luo 《International Journal of Theoretical Physics》2009,48(9):2665-2671
In this paper the generalized conformal symmetries and conserved quantities by Lie point transformations of Hamilton systems
are studied. The necessary and sufficient conditions of conformal symmetry by the action of infinitesimal Lie point transformations
which are simultaneous Lie symmetry are given. This kind type determining equations of conformal symmetry of mechanical systems
are studied. The Hojman conserved quantities of the Hamilton systems under infinitesimal special transformations are obtained.
The relations between conformal symmetries and the Lie symmetries are derived for Hamilton systems. Finally, as application
of the conformal symmetries, an illustration example is introduced. 相似文献
18.
Yan E 《International Journal of Theoretical Physics》2012,51(1):176-184
We study the hidden conformal symmetry of extremal linear Einstein-Maxwell-dilaton-axion black hole. After introduced a new
set of conformal coordinates we find that if focusing on the near-horizon region, for the massless scalar scattering in the
low-frequency limit, there exists hidden conformal symmetry on the solution space, and the real-time correlator is also agree
with the conformal fields theory expectations. 相似文献
19.
Ilija Lukačević 《General Relativity and Gravitation》1990,22(7):721-734
Space-times conformal to physical space-time are considered, assuming the nongravitational energy is conservative after the conformal transformation. Necessary and sufficient conditions satisfied by the conformal factor axe found for a given type of transformation of the energy tensor. The weak gravitational field is defined and the coordinate conditions for the existence of conformal factors in such a field are obtained. 相似文献
20.
Conformal invariance and conserved quantities of a general holonomic system with variable mass
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Conformal invariance and conserved quantities of a general
holonomic system with variable mass are studied. The definition and
the determining equation of conformal invariance for a general
holonomic system with variable mass are provided. The conformal
factor expression is deduced from conformal invariance and Lie
symmetry. The relationship between the conformal invariance and the
Lie symmetry is discussed, and the necessary and sufficient
condition under which the conformal invariance would be the Lie
symmetry of the system under an infinitesimal one-parameter
transformation group is deduced. The conserved quantities of the
system are given. An example is given to illustrate the application
of the result. 相似文献