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Progress in Differential Geometry
Edited by: Katsuhiro Shiohama
A publication of the Mathematical Society of Japan.
Advanced Studies in Pure Mathematics
1993; 505 pp; hardcover
Volume: 22
ISBN-10: 4-314-10105-9
ISBN-13: 978-4-314-10105-9
Order Code: ASPM/22

This volume brings together twenty-five research papers and two survey articles on differential geometry and global analysis, areas in which Japanese differential geometers have recently made great progress. Urakawa's paper is a deep and comprehensive survey on recent results and open problems in differential geometry, including Green functions and Liouville type theorems. Yamaguchi's survey deals with the Lie algebra of all infinitesimal automorphisms of a differential system on a manifold and presents basic material on the geometry of differential systems and simple graded Lie algebras over the real or complex numbers. The research articles cover such topics as minimal surfaces, submanifold theory, analysis on manifolds, \(L^2\)-cohomology theory, and Riemannian geometry. This book will appeal to mathematicians interested in modern differential geometry, as well as to graduate students who are looking for a good overview of some of the main trends in this field.

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 analysis, and mathematicians interested in modern differential geometry.

Table of Contents

  • K. Enomoto -- Compactification of submanifolds in Euclidean space by the inversion
  • H. Fujimoto -- Gauss maps of complete minimal surfaces
  • N. Innami -- Applications of Jacobi and Riccati equations along flows to Riemannian geometry
  • G. Ishikawa -- Maslov class of an isotropic map-germ arising from one-dimensional symplectic reduction
  • T. Iwai and Y. Uwano -- On symmetry groups of the MIC-Kepler problem and their unitary irreducible representations
  • S. Izumiya -- Geometric singularities for Hamilton-Jacobi equation
  • T. Kakehi and C. Tsukamoto -- Characterization of images of Radon transforms
  • M. Koiso -- A uniqueness result for minimal surfaces in \(S^3\)
  • T. Koda and K. Sekigawa -- Self-dual Einstein Hermitian surfaces
  • H. Omori, Y. Maeda, and A. Yoshioka -- Non-commutative complex projective space
  • Y. Matsushita -- Some remarks on fields of \(2\)-planes on compact smooth \(4\)-manifolds
  • R. Miyaoka -- A note on Lie contact manifolds
  • K. Nagatomo -- Rational solutions of the Ernst equation
  • H. Naitoh -- Submanifolds of symmetric spaces and Gauss maps
  • Y. Nakamura -- Lax equations associated with a least squares problem and compact Lie algebras
  • M. Okada -- Green function on self-similar trees
  • K. Ono -- On a theorem of Edmonds
  • T. Ohsawa -- On the \(L^2\) cohomology groups of isolated singularities
  • Y. Se-ashi -- A geometric construction of Laguerre-Forsyth's canonical forms of linear ordinary differential equations
  • K. Shiohama and M. Tanaka -- The length function of geodesic parallel circles
  • T. Shioya -- Diameter and area estimates for \(S^2\) and \(P^2\) with nonnegatively curved metrics
  • K. Sugahara -- On the poles of Riemannian manifolds of nonnegative curvature
  • S. Takakuwa -- Bubbling of minimizing sequences for prescribed scalar curvature problem
  • H. Urakawa -- Geometry of Laplace-Beltrami operator on a complete Riemannian manifold
  • K. Yagi -- Super Lie groups
  • K. Yamaguchi -- Differential systems associated with simple graded Lie algebras
  • T. Yamaguchi -- Tits metric and visibility axiom
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