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CR-Geometry and Overdetermined Systems
Edited by: Takao Akahori, Himeji Institute of Technology, Hyogo, Japan, Gen Komatsu, Osaka University, Osaka, Japan, Kimio Miyajima, Kagoshima University, Kagoshima-shi, Japan, Makoto Namba, Osaka University, Osaka, Japan, and Keizo Yamaguchi, Hokkaido University, Sapporo, Japan
A publication of the Mathematical Society of Japan.
Advanced Studies in Pure Mathematics
1997; 418 pp; hardcover
Volume: 25
ISBN-10: 4-314-10127-X
ISBN-13: 978-4-314-10127-1
List Price: US$76
Member Price: US$60.80
Order Code: ASPM/25
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This volume consists of survey articles and research papers on the most recent developments of CR-geometry and overdetermined systems. Some of the papers are based on the lectures delivered at a conference of the same title. The volume contains notes from three lectures on the invariant theory of the Bergman kernel, and on the deformation of CR structures with applications. Other papers, original or expository, are recent contributions on important problems in complex geometry of differential geometric aspects of analysis, and many of them are related to CR-geometry. This volume offers timely and useful information on the subject area.

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 and research mathematicians interested in several complex variables and analytic spaces.

Table of Contents

  • T. Akahori -- Deformation theory of CR-structures and its application to deformations of isolated singularities I
  • J. Bland and T. Duchamp -- Deformation theory for the hyperplane line bundle on \(P^1\)
  • D. DeTurck and H. Goldschmidt -- Aspects of prescribing Ricci curvature
  • C. L. Epstein -- Deformations of singularities, complex manifolds and CR-structures
  • T. Garrity and R. Mizner -- Vector-valued forms and CR geometry
  • H. Gasqui and H. Goldschmidt -- The infinitesimal spectral rigidity of the real Grassmannians of rank two
  • J. F. Glazebrook and D. Sundararaman -- On deformations of self-dual vector bundles over quaternionic manifolds
  • C.-K. Han and J.-N. Yoo -- A method of prolongation of tangential Cauchy-Riemann equations
  • K. Hirachi and G. Komatsu -- Invariant theory of the Bergman kernel
  • L. Lempert -- Spaces of Cauchy-Riemann manifolds
  • H. S. Luk and S. S. T. Yau -- Some remarks on compact strongly pseudoconvex CR manifolds
  • K. Miyajima -- Deformation theory of CR-structures and its application to deformations of isolated singularities II
  • T. Ohsawa -- A report on isolated singularities by transcendental methods
  • D. H. Phong and R. Silvotti -- The fusion matrix and the Verlinde loop operators in conformal field theory
  • T. Sasaki, K. Yamaguchi, and M. Yoshida -- On the rigidity of differential systems modelled on Hermitian symmetric spaces and disproofs of a conjecture concerning modular interpretations of configuration spaces
  • N. K. Stanton -- Infinitesimal CR automorphisms
  • H. Umemura -- Lie-Drach-Vessiot theory--Infinite dimensional differential Galois theory
  • J. M. Veloso -- Prolongation projection commutativity theorem
  • S. M. Webster -- A complex Frobenius problem
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