Progress in Differential Geometry: (No. 22 Advanced Studies in Pure Mathematics)

This volume brings together 25 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 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 should 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.

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