共查询到20条相似文献,搜索用时 328 毫秒
1.
In the language of tensor analysis on differentiable manifolds, we present a reduction method of integrability structures, and apply it to recover some well-known hierarchies of integrable nonlinear evolution equations.This research has been partially supported by the Italian Ministry of Public Education 相似文献
2.
Marco Pedroni 《Letters in Mathematical Physics》1995,35(4):291-302
We show that the Drinfeld-Sokolov reduction is equivalent to a bi-Hamiltonian reduction, in the sense that these two reductions, although different, lead to the same reduced Poisson (more correctly, bi-Hamiltonian) structure. In order to do this, we heavily use the fact that they are both particular cases of a Marsden-Ratiu reduction.This work has been supported by the Italian MURST and by the GNFM of the Italian CNR. 相似文献
3.
4.
The version of Marsden-Ratiu reduction theorem for Nambu-Poisson manifolds by a regular distribution has been studied by Ibáñez et al. In this paper we show that the reduction is always ensured unless the distribution is zero. Next we extend the more general Falceto-Zambon Poisson reduction theorem for Nambu-Poisson manifolds. Finally, we define gauge transformations of Nambu-Poisson structures and show that these transformations commute with the reduction procedure. 相似文献
5.
Reduction of Poisson manifolds 总被引:9,自引:0,他引:9
Reduction in the category of Poisson manifolds is defined and some basic properties are derived. The context is chosen to include the usual theorems on reduction of symplectic manifolds, as well as results such as the Dirac bracket and the reduction to the Lie-Poisson bracket.Research supported by DOE contract DE-AT03-85ER 12097.Supported by an A. P. Sloan Foundation fellowship. 相似文献
6.
《Journal of Geometry and Physics》2001,37(3):262-271
It is shown how one can do symplectic reduction for locally conformal symplectic manifolds, especially with an action of a Lie group. This generalizes well-known procedures for symplectic manifolds to the slightly larger class of locally conformal symplectic manifolds. The whole setting is very conformally invariant. 相似文献
7.
We study a class of deformations of infinite-dimensional Poisson manifolds of hydrodynamic type which are of interest in the theory of Frobenius manifolds. We prove two results. First, we show that the second cohomology group of these manifolds, in the Poisson-Lichnerowicz cohomology, is essentially trivial. Then, we prove a conjecture of B. Dubrovin about the triviality of homogeneous formal deformations of the above manifolds.Work sponsored by the Italian Ministry of Research under the project 40%: Geometry of Integrable Systems.Acknowledgements. We sincerely thank B. Dubrovin for introducing us to the problem of deformation of Poisson manifolds of hydrodynamic type. We also thank G. Falqui for many useful discussions. We finally thank the Istituto Nazionale di Alta Matematica of Rome, who supported a meeting on the geometry of Frobenius manifolds, giving us the occasion to meet all together and discuss the problem. 相似文献
8.
Suresh Govindarajan 《Letters in Mathematical Physics》1996,37(4):375-383
Recently, certain higher-dimensional complex manifolds were obtained by S. Govindarajan [1] by associating a higher dimensional uniformisation to the generalised Teichmüller spaces of Hitchin. The extra dimensions are provided by the times of the generalised KdV hierarchy. In this Letter, we complete the proof that these manifolds provide the analog of superspace for W-gravity and that W-symmetry linearises on these spaces. This is done by explicitly constructing the relationship between the Beltrami differentials which naturally occur in the higher-dimensional manifolds and the Beltrami differentials which occur in W-gravity. This also resolves an old puzzle regarding the relationship between KdV flow. and W-diffeomorphisms.Dedicated to the memory of Claude Itzykson. 相似文献
9.
Energy transfer processes are very important in solid-state laser systems because they can cause an enhancement of the luminescence
emission resulting in a reduction of the laser threshold. In this work, a detailed investigation to understand the basic processes
of energy transfer between Tm and Ho ions in LiYF4, a solid-state laser crystal, was made. Data includes absorption, luminescence excitation and response to pulsed excitation.
Dynamics of the energy transfer was analyzed by considering the kinetic evolution of the emissions of both ions. It was found
that the energy transfer process between the 3
F
4 spectral manifold of Tm and the 5
I
7 spectral manifold of Ho results in thermal equilibration of these two manifolds.
Received: 20 May 1999 / Revised version: 20 August 1999 / Published online: 27 January 2000 相似文献
10.
A.K. Prykarpatsky J.A. Zagrodziński D.L. Blackmore 《Reports on Mathematical Physics》1997,40(3):539-549
A general approach to building integrable Lax-type flows on Grassmann manifolds, based on the momentum mapping reduction theory, is developed. All of the flows are shown to be Hamiltonian with respect to different symplectic structures generated by dual special Hamiltonian actions on Grassmann manifolds. As a by-product of the approach a natural connection associated with dual momentum mappings is constructed explicitly via one Uhlmann's procedure. 相似文献
11.
Gregorio Falqui 《Reports on Mathematical Physics》2002,50(3):395
We formulate and discuss a reduction theorem for Poisson pencils associated with a class of integrable systems, defined on bi-Hamiltonian manifolds, recently studied by Gel'fand and Zakharevich. The reduction procedure is suggested by the bi-Hamiltonian approach to the separation of variables problem. 相似文献
12.
Wu-yen Chuang Shamit Kachru Alessandro Tomasiello 《Communications in Mathematical Physics》2007,274(3):775-794
We construct a class of symplectic non-Kähler and complex non-Kähler string theory vacua, extending and providing evidence for an earlier suggestion by Polchinski and Strominger. The class admits a mirror pairing by construction. Comparing hints from a variety of sources, including ten-dimensional supergravity and KK reduction on SU(3)-structure manifolds, suggests a picture in which string theory extends Reid’s fantasy to connect classes of both complex non-Kähler and symplectic non-Kähler manifolds. 相似文献
13.
General boundary conditions (branes') for the Poisson sigma model are studied. They turn out to be labeled by coisotropic submanifolds of the given Poisson manifold. The role played by these boundary conditions both at the classical and at the perturbative quantum level is discussed. It turns out to be related at the classical level to the category of Poisson manifolds with dual pairs as morphisms and at the perturbative quantum level to the category of associative algebras (deforming algebras of functions on Poisson manifolds) with bimodules as morphisms. Possibly singular Poisson manifolds arising from reduction enter naturally into the picture and, in particular, the construction yields (under certain assumptions) their deformation quantization. 相似文献
14.
It is shown that the singular Poisson reduction procedure can be improved for a large class of situations. In addition, Poisson reduction of orbit type manifolds is carried out in detail. 相似文献
15.
Mihai Visinescu 《Physics of Particles and Nuclei》2012,43(5):717-719
We investigate the reduction and unfolding of dynamical systems with gauge symmetries. An application is provided by a non relativistic point charge in the field of a Dirac monopole. The corresponding dynamical system possessing a Kepler type symmetry is associated with the Taub-NUT metric using a reduction procedure of symplectic manifolds with symmetries. The reverse of the reduction procedure is done by stages performing the unfolding of the gauge transformation followed by the Eisenhart lift in connection with scalar potentials. 相似文献
16.
We develop the theory of generalized bi-Hamiltonian reduction. Applying this theory to a suitable loop algebra we recover a generalized Drinfeld–Sokolov reduction. This gives a way to construct new examples of algebraic Frobenius manifolds. 相似文献
17.
《Journal of Geometry and Physics》2002,41(3):181-195
A reduction theorem for Jacobi–Nijenhuis manifolds is established and its relation with the reduction of homogeneous Poisson–Nijenhuis structures is shown. Reduction under Lie group actions is also studied. 相似文献
18.
Dmitry Roytenberg 《Letters in Mathematical Physics》2007,79(2):143-159
We give a detailed exposition of the Alexandrov–Kontsevich–Schwarz– Zaboronsky superfield formalism using the language of
graded manifolds. As a main illustrating example, to every Courant algebroid structure we associate canonically a three-dimensional
topological sigma-model. Using the AKSZ formalism, we construct the Batalin–Vilkovisky master action for the model.
相似文献
19.
Vector fields whose flow preserves a symplectic form up to a constant, such as simple mechanical systems with friction, are called “conformal”. We develop a reduction theory for symmetric conformal Hamiltonian systems, analogous to symplectic reduction theory. This entire theory extends naturally to Poisson systems: given a symmetric conformal Poisson vector field, we show that it induces two reduced conformal Poisson vector fields, again analogous to the dual pair construction for symplectic manifolds. Conformal Poisson systems form an interesting infinite-dimensional Lie algebra of foliate vector fields. Manifolds supporting such conformal vector fields include cotangent bundles, Lie–Poisson manifolds, and their natural quotients. 相似文献
20.
D.V. Boulatov 《Communications in Mathematical Physics》1997,186(2):295-322
A quantum deformation of 3-dimensional lattice gauge theory is defined by applying the Reshetikhin-Turaev functor to a Heegaard
diagram associated to a given cell complex. In the root-of-unity case, the construction is carried out with a modular Hopf
algebra. In the topological (weak-coupling) limit, the gauge theory partition function gives a 3-fold invariant, coinciding
in the simplicial case with the Turaev-Viro one. We discuss bounded manifolds as well as links in manifolds. By a dimensional
reduction, we obtain a q-deformed gauge theory on Riemann surfaces and find a connection with the algebraic Alekseev-Grosse-Schomerus approach.
Received: 29 April 1996 / Accepted: 24 September 1996 相似文献