Lie Groups, Geometric Structures and Differential Equations: One Hundred Years After Sophus Lie (Advanced Studies in Pure Mathematics No. 37)
By: Hajime Sato (editor), Keizo Yamaguchi (editor), Tohru Morimoto (editor)Hardback
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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 Elie 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.
Levi-flat minimal hypersurfaces in two-dimensional complex space forms by R. L. Bryant Partially integrable almost CR manifolds of CR dimension and codimension two by A. Cap and G. Schmalz Some remarks on the infinitesimal rigidity of the complex quadric by J. Gasqui and H. Goldschmidt On one-parametric families of Backlund transformations by S. Igonin and J. Krasil'shchik Submanifolds with degenerate Gauss mappings in spheres by G. Ishikawa, M. Kimura, and R. Miyaoka Complete integrability of the coupled KdV-mKdV system by P. Kersten and J. Krasil'shchik An approach to the Cartan geometry I: Conformal Riemann manifolds by M. Kuranishi Differential algebra and differential geometry by B. Malgrange Lie algebras, geometric structures and differential equations on filtered manifolds by T. Morimoto Cayley transforms and symmetry conditions for homogeneous Siegel domains by T. Nomura The canonical contact form by P. J. Olver Associativity breaks down in deformation quantization by H. Omori Lifting of holomorphic actions on complex supermanifolds by A. L. Onishchik Contact transformations and their Schwarzian derivatives by T. Ozawa and H. Sato Isometric immersions into complex projective space by P. Tomter Geometry of higher order differential equations of finite type associated with symmetric spaces by K. Yamaguchi and T. Yatsui Contact Weyl manifold over a symplectic manifold by A. Yoshioka.
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