Advanced Studies in Pure Mathematics 1993; 505 pp; hardcover Volume: 22 ISBN10: 4314101059 ISBN13: 9784314101059 Order Code: ASPM/22  This volume brings together twentyfive 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 postpublication. Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS. Readership 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 mapgerm arising from onedimensional symplectic reduction
 T. Iwai and Y. Uwano  On symmetry groups of the MICKepler problem and their unitary irreducible representations
 S. Izumiya  Geometric singularities for HamiltonJacobi 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  Selfdual Einstein Hermitian surfaces
 H. Omori, Y. Maeda, and A. Yoshioka  Noncommutative 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 selfsimilar trees
 K. Ono  On a theorem of Edmonds
 T. Ohsawa  On the \(L^2\) cohomology groups of isolated singularities
 Y. Seashi  A geometric construction of LaguerreForsyth'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 LaplaceBeltrami 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
