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Lie Groups, Geometric Structures and Differential Equations--One Hundred Years After Sophus Lie
Edited by: Tohru Morimoto, Nara Women's University, Nara City, Japan, Hajime Sato, Science University of Tokyo, Japan, and Keizo Yamaguchi, Hokkaido University, Sapporo, Japan
A publication of the Mathematical Society of Japan.
Advanced Studies in Pure Mathematics
2002; 493 pp; hardcover
Volume: 37
ISBN-10: 4-931469-21-3
ISBN-13: 978-4-931469-21-1
List Price: US$110
Member Price: US$88
Order Code: ASPM/37
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The blending of algebra, geometry, and differential equations has a long and distinguished history, dating back to the work of Sophus Lie and Élie Cartan. Overviewing the depth of their influence over the past 100 years presents a formidable challenge. A conference was held on the centennial of Lie's death to reflect upon and celebrate his pursuits, later developments, and what the future may hold. This volume showcases the contents, atmosphere, and results of that conference.

Of particular importance are two survey articles: Morimoto develops a synthetic study of Lie groups, geometric structures, and differential equations from a unified viewpoint of nilpotent geometry. Yamaguchi and Yatsui discuss the geometry of higher order differential equations of finite type. Contributed research articles cover a wide range of disciplines, from geometry of differential equations, CR-geometry, and differential geometry to topics in mathematical physics.

This volume is intended for graduate students studying differential geometry and analyis and advanced graduate students and researchers interested in an overview of the most recent progress in these fields.

Volumes in this series are freely available electronically 5 years post-publication.

Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS.


Graduate students studying differential geometry and advanced graduate students and researchers interested in overviewing the most recent progress in these fields.

Table of Contents

  • R. L. Bryant -- Levi-flat minimal hypersurfaces in two-dimensional complex space forms
  • A. Čap and G. Schmalz -- Partially integrable almost CR manifolds of CR dimension and codimension two
  • J. Gasqui and H. Goldschmidt -- Some remarks on the infinitesimal rigidity of the complex quadric
  • S. Igonin and J. Krasil'shchik -- On one-parametric families of Bäcklund transformations
  • G. Ishikawa, M. Kimura, and R. Miyaoka -- Submanifolds with degenerate Gauss mappings in spheres
  • P. Kersten and J. Krasil'shchik -- Complete integrability of the coupled KdV-mKdV system
  • M. Kuranishi -- An approach to the Cartan geometry I: Conformal Riemann manifolds
  • B. Malgrange -- Differential algebra and differential geometry
  • T. Morimoto -- Lie algebras, geometric structures and differential equations on filtered manifolds
  • T. Nomura -- Cayley transforms and symmetry conditions for homogeneous Siegel domains
  • P. J. Olver -- The canonical contact form
  • H. Omori -- Associativity breaks down in deformation quantization
  • A. L. Onishchik -- Lifting of holomorphic actions on complex supermanifolds
  • T. Ozawa and H. Sato -- Contact transformations and their Schwarzian derivatives
  • P. Tomter -- Isometric immersions into complex projective space
  • K. Yamaguchi and T. Yatsui -- Geometry of higher order differential equations of finite type associated with symmetric spaces
  • A. Yoshioka -- Contact Weyl manifold over a symplectic manifold
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