Differential-geometric Poisson Brackets on a Lattice
نویسنده
چکیده
The concept of differential-geometric Poisson brackets (DGPB) was introduced in [i] in connection with an investigation of the properties of Poisson brackets of hydrodynamic type [2] and their generalizations. Recall that homogeneous DGPBs of m-th order on a phase space of fields u i @),i = i ..... N,x ~ ~ (in this note we confine attention to the spatially onedimensional case), taking values in a manifold~ N, are defined by
منابع مشابه
Hydrodynamics of Weakly Deformed Soliton Lattices. Differential Geometry and Hamiltonian Theory Hydrodynamics of Weakly Deformed Soliton Lattices. Differential Geometry and Hamiltonian Theory
CONTENTS Introduction 35 Chapter I. Hamiltonian theory of systems of hydrodynamic type 45 § 1. General properties of Poisson brackets 45 §2. Hamiltonian formalism of systems of hydrodynamic type and 55 Riemannian geometry §3. Generalizations: differential-geometric Poisson brackets of higher orders, 66 differential-geometric Poisson brackets on a lattice, and the Yang-Baxter equation §4. Rieman...
متن کاملGeometric Poisson Brackets on Grassmannians and Conformal Spheres
In this paper we relate the geometric Poisson brackets on the 2Grassmannian in R4 and on the (2, 2) Möbius sphere. We show that, when written in terms of local moving frames, the geometric Poisson bracket on the Möbius sphere does not restrict to the space of differential invariants of Schwarzian type. But when the concept of conformal natural frame is transported from the conformal sphere into...
متن کاملGeometric Hamiltonian Structures on Flat Semisimple Homogeneous Manifolds
In this paper we describe Poisson structures defined on the space of Serret-Frenet equations of curves in a flat homogeneous space G/H where G is semisimple. These structures are defined via Poisson reduction from Poisson brackets on Lg∗, the space of Loops in g∗. We also give conditions on invariant geometric evolution of curves in G/H which guarantee that the evolution induced on the differen...
متن کاملMoving Frames, Geometric Poisson Brackets and the Kdv-schwarzian Evolution of Pure Spinors
In this paper we describe a non-local moving frame along a curve of pure spinors in O(2m, 2m)/P , and its associated basis of differential invariants. We show that the space of differential invariants of Schwarzian-type define a Poisson submanifold of the spinor Geometric Poisson brackets. The resulting restriction is given by a decoupled system of KdV Poisson structures. We define a generaliza...
متن کاملDescription of compatible differential - geometric Poisson brackets of the first order
One of the most interesting questions of the classical differential geometry which has appeared at studying of semi-Hamiltonian systems of hydrodynamical type is the description of the surfaces admitting not trivial deformations with preservation of principal directions and principal curvatures. Then the number of essential parameters on which such deformations depend, is actually equal to numb...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004