Symmetries and Overdetermined Systems of Partial Differential Equations / Edition 1

Symmetries and Overdetermined Systems of Partial Differential Equations / Edition 1

by Michael Eastwood
     
 

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ISBN-10: 0387738304

ISBN-13: 9780387738307

Pub. Date: 11/28/2007

Publisher: Springer New York

Symmetries in various forms pervade mathematics and physics. Globally, there are the symmetries of a homogeneous space induced by the action of a Lie group. Locally, there are the infinitesimal symmetries induced by differential operators, including not only those of first order but of higher order too. This three-week summer program considered the symmetries

Overview

Symmetries in various forms pervade mathematics and physics. Globally, there are the symmetries of a homogeneous space induced by the action of a Lie group. Locally, there are the infinitesimal symmetries induced by differential operators, including not only those of first order but of higher order too. This three-week summer program considered the symmetries preserving various natural geometric structures. Often these structures are themselves derived from partial differential equations whilst their symmetries turn out to be constrained by overdetermined systems. This leads to further topics including separation of variables, conserved quantities, superintegrability, parabolic geometry, representation theory, the Bernstein-Gelfand-Gelfand complex, finite element schemes, exterior differential systems and moving frames.

There are two parts to the Proceedings. The articles in the first part are expository but all contain significant new material. The articles in the second part are concerned with original research. All articles were thoroughly refereed and the range of interrelated work ensures that this will be an extremely useful collection.

These Proceedings are dedicated to the memory of Thomas P. Branson who played a leading role in the conception and organization of this Summer Program but did not live to see its realization.

Product Details

ISBN-13:
9780387738307
Publisher:
Springer New York
Publication date:
11/28/2007
Series:
IMA Volumes in Mathematics and its Applications Series, #144
Edition description:
2008
Pages:
568
Product dimensions:
6.30(w) x 9.30(h) x 1.20(d)

Table of Contents

Foreword     v
In memory of Professor Thomas P. Branson     vii
Preface     ix
Expository Articles
Overdetermined systems, conformal differential geometry, and the BGG complex   Andreas Cap     1
Generalized Wilczynski invariants for non-linear ordinary differential equations   Boris Doubrov     25
Notes on projective differential geometry   Michael Eastwood     41
Ambient metric construction of CR invariant differential operators   Kengo Hirachi     61
Fine structure for second order superintegrable systems   Ernie G. Kalnins   Jonathan M. Kress   Willard Miller, Jr.     77
Differential geometry of submanifolds of projective space   Joseph M. Landsberg     105
Pseudo-groups, moving frames, and differential invariants   Peter J. Olver   Juha Pohjanpelto     127
Geometry of linear differential systems towards contact geometry of second order   Keizo Yamaguchi     151
Research Articles
On geometric properties of joint invariants of Killing tensors   Caroline M. Adlam   Raymond G. McLenaghan   Roman G. Smirnov     205
Hamiltonian curve flows in Lie groups G [subset or is implied by] U(N) and vector NLS, mKdV, sine-Gordon soliton equations   Stephen C. Anco     223
Conformal Killing spinors and the holonomy problem in Lorentzian geometry - A survey of new results -   Helga Baum     251
Projective-type differential invariants for curves and their associated PDES of KDV type   Gloria Mari Beffa     265
Algebraic construction of the quadratic first integrals for a special class of orthogonal separable systems   Sergio Benenti     277
Geometry of non-regular separation   Claudia Chanu     305
Higher symmetries of the square of the Laplacian   Michael Eastwood   Thomas Leistner     319
Metric connections in projective differential geometry   Michael Eastwood   Vladimir Matveev     339
Exterior differential systems with symmetry   Mark E. Fels     351
Partially invariant solutions to ideal magnetohydrodynamics   Sergey V. Golovin     367
Invariant prolongation and detour complexes   A. Rod Gover     383
Inhomogeneous ambient metrics   C. Robin Graham   Kengo Hirachi     403
Pfaffian systems of Frobenius type and solvability of generic overdetermined PDE systems   Chong-Kyu Han     421
Exact and quasi-exact solvability of second order superintegrable quantum systems   Ernie G. Kalnins   Willard Miller, Jr.   George S. Pogosyan     431
A remark on unitary conformal holonomy   Felipe Leitner     445
Polynomial associative algebras for quantum superintegrable systems with a third order integral of motion   Ian Marquette     461
Separation of variables for systems of first-order partial differential equations and the Dirac equation in two-dimensional manifolds   Raymond G. McLenaghan   Giovanni Rastelli     471
Differential systems associated with tableaux over Lie algebras   Emilio Musso   Lorenzo Nicolodi     497
Conformal structures with explicit ambient metrics and conformal G[subscript 2] holonomy   Pawel Nurowski     515
Deformations of quadratic algebras, the Joseph ideal for classical Lie algebras, and special tensors   Petr Somberg     527
Analogues of the Dolbeault complex and the separation of variables   Vladimir Soucek     537
List of workshop participants     551

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