共查询到20条相似文献,搜索用时 15 毫秒
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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
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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
4.
Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. The relationship between the conformal invariance and the Lie symmetry is given, and the necessary and sufficient condition that the conformal invarianee would be the Lie symmetry under the infinitesimal transformations is provided. Secondly, a new type of conserved quantities of the conformal invariance are obtained by using the Lie symmetry of the system. Lastly, an example is given to illustrate the application of the results. 相似文献
5.
Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. The relationship between the conformal invariance and the Lie symmetry is given, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry under the infinitesimal transformations is provided.Secondly, a new type of conserved quantities of the conformal invariance are obtained by using the Lie symmetry of the system. Lastly, an example is given to illustrate the application of the results. 相似文献
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The difference between the Riemann and Lorentz spinor manifolds of four dimensions is that the Dirac operator of the former is elliptic and that of the latter is hyperbolic.Moreover the spinor group of the former is a compact group and that of the latter is a noncompact group,which is isomorphic to SL(2,C).Hence the results and their interpretation coming from the two theories would be different.In this short note we study only the Lorentz spinor manifold and,especially,the solutions of Einstein-Dirac equations on the conformal space,which is closely related to the AdS/CFT correspondence. 相似文献
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Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space 下载免费PDF全文
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
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The Bach equation and the equation of geometrodynamics are based on two quite different physical motivations, but in both approaches, the conformal properties of gravitation play the key role. In this paper we present an analysis of the relation between these two equations and show that the solutions of the equation of geometrodynamics are of a more general nature. We show the following non-trivial result: there exists a conformally invariant Lagrangian, whose field equation generalizes the Bach equation and has as solutions those Ricci tensors which are solutions to the equation of break geometrodynamics. 相似文献
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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
11.
Conformal invariance and generalized Hojman conserved quantities of mechanico-electrical systems 下载免费PDF全文
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
12.
Conformal invariance and conserved quantities of Appell systems under second-class Mei symmetry 总被引:2,自引:0,他引:2 下载免费PDF全文
In this paper we introduce the new concept of the conformal invariance and the conserved quantities for Appell systems under second-class Mei symmetry. The one-parameter infinitesimal transformation group and infinitesimal transformation vector of generator are described in detail. The conformal factor in the determining equations under second-class Mei symmetry is found. The relationship between Appell system’s conformal invariance and Mei symmetry are discussed. And Appell system’s conformal invariance under second-class Mei symmetry may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Lastly, an example is provided to illustrate the application of the result. 相似文献
13.
A new algorithm for the Petrov classification of the Weyl tensor is introduced. It is similar to the Letniowski-McLenaghan algorithm [1] when some of the 's are zero, but offers a completely new approach when all of the 's are nonzero. In all cases, new code in Maple has been implemented. 相似文献
14.
Conformal invariance and conserved quantities of a general holonomic system with variable mass 下载免费PDF全文
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
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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
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Conformal invariance, Noether symmetry, Lie symmetry and conserved quantities of Hamilton systems 下载免费PDF全文
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
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This paper studies a conformal invariance and an integration of first-order differential equations. It obtains the corresponding infinitesimal generators of conformal invariance by using the symmetry of the differential equations, and expresses the differential equations by the equations of a Birkhoff system or a generalized Birkhoff system. If the infinitesimal generators are those of a Noether symmetry, the conserved quantity can be obtained by using the Noether theory of the Birkhoff system or the generalized Birkhoff system. 相似文献