Differential and Riemannian geometry Books

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Exact solutions to Einstein's equations have been useful for the understanding of general relativity in many respects. They have led to such physical concepts as black holes and event horizons, and helped to visualize...

Matrix-valued data sets - so-called second order tensor fields - have gained significant importance in scientific visualization and image processing due to recent developments such as diffusion tensor imaging. This book is the...

This book develops a modern presentation of Continuum Mechanics, oriented towards numerical applications in the ?elds of nonlinear analysis of solids, structures and ?uids. Kinematics of the continuum deformation, including...

This volume reflects the growing collaboration between mathematicians and theoretical physicists to treat the foundations of quantum field theory using the mathematical tools of q-deformed algebras and noncommutative...

Application of the concepts and methods of topology and geometry have led to a deeper understanding of many crucial aspects in condensed matter physics, cosmology, gravity and particle physics. This book can be considered an...

Projective duality is a very classical notion naturally arising in various areas of mathematics, such as algebraic and differential geometry, combinatorics, topology, analytical mechanics, and invariant theory, and the results in this field were until...

The book covers topics in the theory of algebraic transformation groups and algebraic varieties which are very much at the frontier of mathematical research.

The book gathers contributions from the fourth conference on Information Geometry and its Applications, which was held on June 12-17, 2016, at Liblice Castle, Czech Republic on the occasion of Shun-ichi Amari's 80th birthday and was organized by the...

The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for...

This volume collects contributions written bydifferent experts in honor of Prof. Jaime Muñoz Masqué. It covers awide variety of research topics, from differential geometry to algebra, butparticularly focuses on the geometric formulation of...

This volume contains a collection of research papers and useful surveys by experts in the field which provide a representative picture of the current status of this fascinating area. Based on contributions from the VIII International Meeting on...

The theories of V. V. Wagner (1908-1981) on abstractions of systems of binary relations are presented here within their historical and mathematical contexts.  This book contains the first translation from Russian into English of a selection of...

This book presents current research on Ulam stability for functional equations and inequalities. Contributions from renowned scientists emphasize fundamental and new results, methods and techniques. Detailed examples are given to theories to further...

This volume is a tribute to Maxim Kontsevich, one of the most original and influential mathematicians of our time. Maxim's vision has inspired major developments in many areas of mathematics, ranging all the way from probability theory to motives over...

Differential and complex geometry are two central areas of mathematics with a long and intertwined history. This book, the first to provide a unified historical perspective of both subjects, explores their origins and developments from the sixteenth to...

This book presents four survey articles on different topics in mathematical analysis that are closely linked to concepts and applications in physics. Specifically, it discusses global aspects of elliptic PDEs, Berezin-Toeplitz quantization, the stability...

This book includes selected papers presented at the MIMS (Mediterranean Institute for the Mathematical Sciences) - GGTM (Geometry and Topology Grouping for the Maghreb) conference, held in memory of Mohammed Salah Baouendi, a most renowned figure in the...

Honoring Andrei Agrachev's 60th birthday, this volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic...

This book presents the classical theory of curves in the plane and three-dimensional space, and the classical theory of surfaces in three-dimensional space. It pays particular attention to the historical development of the theory and the preliminary...

Andreas Floer died on May 15, 1991 an untimely and tragic death. His visions and far-reaching contributions have significantly influenced the developments of mathematics. His main interests centered on the fields of dynamical...

The topics in this survey volume concern research done on the differential geom­ etry of foliations over the last few years. After a discussion of the basic concepts in the theory of foliations in the first four chapters, the...

Boundary problems constitute an essential field of common mathematical interest, they lie in the center of research activities both in analysis and geometry. This book encompasses material from both disciplines, and focuses on...

This is the first exposition of the quantization theory of singular symplectic (Marsden-Weinstein) quotients and their applications to physics. The reader will acquire an introduction to the various techniques used in this...

The material and references in this extended second edition of "The Topology of Torus Actions on Symplectic Manifolds", published as Volume 93 in this series in 1991, have been updated. Symplectic manifolds and torus actions...

Metric and Differential Geometry grew out of a similarly named conference held at Chern Institute of Mathematics, Tianjin and Capital Normal University, Beijing. The various contributions to this volume cover a broad range of topics in metric and...

This monograph deals with matrix manifolds, i.e., manifolds for which there is a natural representation of their elements as matrix arrays. Classical matrix manifolds (Stiefel, Grassmann and flag manifolds) are studied in a more general setting. It...

This monograph presents the geometric foundations of continuum mechanics. An emphasis is placed on increasing the generality and elegance of the theory by scrutinizing the relationship between the physical aspects and the mathematical notions used in its...

This monograph explores classical electrodynamics from a geometrical perspective with a clear visual presentation throughout. Featuring over 200 figures, readers will delve into the definitions, properties, and uses of directed quantities in classical...

This book pedagogically describes recent developments in gauge theory, in particular four-dimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation...

This monograph systematically explores the theory of rational maps between spheres in complex Euclidean spaces and its connections to other areas of mathematics.  Synthesizing research from the last forty years, the author aims for accessibility by...

This book presents a differential geometric method for designing nonlinear observers for multiple types of nonlinear systems, including single and multiple outputs, fully and partially observable systems, and regular and singular dynamical systems. It is...

What do the classification of algebraic surfaces, Weyl's dimension formula and maximal orders in central simple algebras have in common? All are related to a type of manifold called locally mixed symmetric spaces in this book. The presentation emphasizes...

This book provides an introduction to some aspects of the flourishing field of nonsmooth geometric analysis. In particular, a quite detailed account of the first-order structure of general metric measure spaces is presented, and the reader is introduced...

This textbook offers readers a self-contained introduction to quantitative Tamarkin category theory. Functioning as a viable alternative to the standard algebraic analysis method, the categorical approach explored in this book makes microlocal sheaf...

This monograph is the first one to systematically present a series of local and global estimates and inequalities for differential forms, in particular the ones that satisfy the A-harmonic equations. The presentation focuses on the Hardy-Littlewood,...

In recent years, research in K3 surfaces and Calabi-Yau varieties has seen spectacular progress from both arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics-in particular, in string...

Homogeneous Finsler Spaces is the first book to emphasize the relationship between Lie groups and Finsler geometry, and the first to show the validity in using Lie theory for the study of Finsler geometry problems. This book contains a series of new...

1. Complex manifold.- 2. Almost complex structure.- 3. Complex vector space complexification.- 4. Kähler manifold.- 5. Structure equations of a submanifold.- 6. Submanifolds of a Euclidean space.- 7. Submanifolds of a complex manifold.- 8. The Levi form...

The papers in this volume are an outgrowth of the lectures and informal discussions that took place during the workshop on "The Geometry of Hamiltonian Systems" which was held at MSRl from June 5 to 16, 1989. It was, in some...

Substances possessing heterogeneous microstructure on the nanometer and micron scales are scientifically fascinating and technologically useful. Examples of such substances include liquid crystals, microemulsions, biological...

The theory of foliations of manifolds was created in the forties of the last century by Ch. Ehresmann and G. Reeb [ER44]. Since then, the subject has enjoyed a rapid development and thousands of papers investigating foliations...

curvilinear coordinates. This treatment includes in particular a direct proof of the three-dimensional Korn inequality in curvilinear coordinates. The fourth and last chapter, which heavily relies on Chapter 2, begins by a...

L' inj´ ´ enuit´ ´ mˆ eme d' un regard neuf (celui de la science l'est toujours) peut parfois ´ ´clairer d' un jour nouveau d' anciens probl` emes. J.Monod [77, p. 13] his book is intended as a comprehensive introduction to the...

GU Chaohao The soliton theory is an important branch of nonlinear science. On one hand, it describes various kinds of stable motions appearing in - ture, such as solitary water wave, solitary signals in optical ?bre etc., and...