Differential and Riemannian geometry

Differential geometry, in the classical sense, is developed through the theory of smooth manifolds.

Complex variables is a precise, elegant, and captivating subject.

Lie Theory: Unitary Representations and Compactifications of Symmetric Spaces, a self-contained work by A.

Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics.

This volume contains research and survey articles by well known and respected mathematicians describing recent developments and research trends in differential geometry and topology that have been collected and dedicated in honor of Lieven Vanhecke, as a tribute to his many fruitful and inspiring contributions to these fields.

Differential geometry techniques have very useful and important applications in partial differential equations and quantum mechanics.

One of the world's foremost geometers, Alan Weinstein has made deep contributions to symplectic and differential geometry, Lie theory, mechanics, and related fields.

This concise guide to the differential geometry of curves and surfaces can be recommended to ?

Shows novel and modern ways of solving differential equations using methods from contact and symplectic geometry.

This book introduces D-modules and their applications avoiding all unnecessary over-sophistication.

This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.

This book is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level.

A collection of articles giving overviews and open questions in singularities and their computational aspects.

This book, first published in 2006, details how limit processes can be represented algebraically.

An introduction to Ricci flow suitable for graduate students and research mathematicians.

A thoroughly revised introduction to non-commutative geometry.

Applications covered include image segmentation, shape analysis, image enhancement, and tracking.

This easy-to-read introduction takes the reader from elementary problems through to current research.

This 2007 textbook uses examples, exercises, diagrams, and unambiguous proof, to help students make the link between classical and differential geometries.

This graduate text provides a concise and self-contained introduction to Kähler geometry.

An advanced undergraduate and graduate textbook introducing differential geometry for theoretical physics and applied mathematics.

This corrected and clarified second edition, first published in 2006, includes a new chapter on the Riemannian geometry of surfaces.

This book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere.

Self-contained, richly illustrated account of modern differential geometry applied to integral geometry.

Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry.

Nonlinear Optimization is an intriguing area of study where mathematical theory, algorithms and applications converge to calculate the optimal values of continuous functions.

This self-contained text is an excellent introduction to Lie groups and their actions on manifolds.

This book provides a modern treatment of Lie's geometry of spheres, its applications and the study of Euclidean space.

This book is devoted to the study of scalar and asymptotic scalar derivatives and their applications to the study of some problems considered in nonlinear analysis, in geometry, and in applied mathematics.

Differential forms satisfying the A-harmonic equations have found wide applications in fields such as general relativity, theory of elasticity, quasiconformal analysis, differential geometry, and nonlinear differential equations in domains on manifolds.

This book offers the most comprehensive survey to date of the theory of semiparallel submanifolds.

Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups.

"e;From nothing I have created a new different world,"e; wrote Janos Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today.

Intended for a one year course, this volume serves as a single source, introducing students to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry.

In introducing his essays on the study and understanding of nature and e- lution, biologist Stephen J.

This book presents aspects of a geometric theory of infinite dimensional spaces with major emphasis on retarded functional differential equations.

This book is designed as a textbook for a one-quarter or one-semester graduate course on Riemannian geometry, for students who are familiar with topological and differentiable manifolds.

This text is an elementary introduction to differential geometry.

For more than five decades Bertram Kostant has been one of the major architects of modern Lie theory.

In this book the authors study the differential geometry of varieties with degenerate Gauss maps.

Manifolds are everywhere.

This book provides the first unified examination of the relationship between Radon transforms on symmetric spaces of compact type and the infinitesimal versions of two fundamental rigidity problems in Riemannian geometry.

The title of this book is no surprise for people working in the field of Analytical Mechanics.

This book is written for theoretical and mathematical physicists and mat- maticians interested in recent developments in complex general relativity and their application to classical and quantum gravity.

Despite the fundamental role played by Reshetnyak's work in the theory of surfaces of bounded integral curvature, the proofs of his results were only available in his original articles, written in Russian and often hard to find.

Black holes present one of the most fascinating predictions of Einstein's general theory of relativity.

This book is a new edition of "e;Tensors and Manifolds: With Applications to Mechanics and Relativity"e; which was published in 1992.

Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997.

This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors.