This volume constitutes the proceedings of the third Franco-Japanese symposium on singularities, held in Sapporo in September 2004. It contains not only research papers on the most advanced topics in the field, but also some survey articles which give broad scopes in some areas of the subject. All the articles are carefully refereed for correctness and readability.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America

This graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective. Co-authored by the originator of the world's leading human motion simulator -- "Human Biodynamics Engine," a complex, 264-DOF bio-mechanical system, modeled by differential-geometric tools -- this is the first book that combines modern differential geometry with a wide spectrum of applications, from modern mechanics and physics, via nonlinear control, to biology and human sciences. The book is designed for a two-semester course, which gives mathematicians a variety of applications for their theory and physicists, as well as other scientists and engineers, a strong theory underlying their models.

Pseudo-Riemannian geometry is an active research field not only in differential geometry but also in mathematical physics where the higher signature geometries play a role in brane theory. An essential reference tool for research mathematicians and physicists, this book also serves as a useful introduction to students entering this active and rapidly growing field. The author presents a comprehensive treatment of several aspects of pseudo-Riemannian geometry, including the spectral geometry of the curvature tensor, curvature homogeneity, and Stanilov-Tsankov-Videv theory.

This book provides the first-ever systematic introduction to the theory of Riemannian submersions, which was initiated by Barrett O'Neill and Alfred Gray less than four decades ago. The authors focus their attention on classification theorems when the total space and the fibres have nice geometric properties. Particular emphasis is placed on the interrelation with almost Hermitian, almost contact and quaternionic geometry. Examples clarifying and motivating the theory are included in every chapter. Recent results on semi-Riemannian submersions are also explained. Finally, the authors point out the close connection of the subject with some areas of physics.

This volume contains the courses and lectures given during the workshop on Differential Geometry and Topology held at Alghero, Italy, in June 1992.The main goal of this meeting was to offer an introduction in attractive areas of current research and to discuss some recent important achievements in both the fields. This is reflected in the present book which contains some introductory texts together with more specialized contributions.The topics covered in this volume include circle and sphere packings, 3-manifolds invariants and combinatorial presentations of manifolds, soliton theory and its applications in differential geometry, G-manifolds of low cohomogeneity, exotic differentiable structures on R4, conformal deformation of Riemannian manifolds and Riemannian geometry of algebraic manifolds.

This book takes a historical approach to Einstein's General Theory of Relativity and shows the importance that geometry has to the theory. Starting from simpler and more general considerations, it goes on to detail the latest developments in the field and considers several cutting-edge research areas. It discusses Einstein's theory from a geometrical and a field theoretic viewpoint, before moving on to address gravitational waves, black holes and cosmology.

This book describes applications of the PDE methods to the construction and study of Ricci-flat metrics with special holonomy. Particular attention is paid to Ricci-flat Kahler (Calabi-Yau) structures on complex manifolds and hyper-Kahler structures on K3 surfaces. Complex manifolds are also an object of study in algebraic geometry and special consideration is given to the interplay between some well-known algebraic varieties (K3 surfaces, Fano threefolds, for example) and differential-geometric structures of special holonomy. The interplay between the gluing techniques, Calabi-Yau theory and algebraic geometry is further illuminated by the connected sum construction of compact 7-dimensional manifolds with holonomy G2.