Symmetries and overdetermined systems of partial differential equations / Michael Eastwood, Willard Miller, Jr., editors.

Format:

Book

Contributor:

Eastwood, Michael G.

Miller, Willard

Hazel M. Hussong Fund.

Series:

IMA volumes in mathematics and its applications ; 144.

IMA volumes in mathematics and its applications ; 144

Language:

English

Subjects (All):

Differential equations, Partial--Congresses.

Differential equations, Partial.

Symmetry (Mathematics)--Congresses.

Symmetry (Mathematics).

Global analysis (Mathematics)--Congresses.

Global analysis (Mathematics).

Geometry, Differential--Congresses.

Geometry, Differential.

Genre:

Conference papers and proceedings.

Physical Description:

xv, 554 pages : illustrations ; 25 cm.

Place of Publication:

New York : Springer, [2008]

Summary:

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.

Contents:

In memory of Professor Thomas P. Branson vii

Part I 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

Part II 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.

Notes:

Papers presented at the IMA Summer Program held July 17-August 4, 2006 and dedicated to the memory of Thomas P. Branson.

Includes bibliographical references.

Local Notes:

Acquired for the Penn Libraries with assistance from the Hazel M. Hussong Fund.

ISBN:

9780387738307

0387738304

OCLC:

212375554

Online:

Publisher description