Differential and Riemannian geometry

The subjects of stochastic processes, information theory, and Lie groups are usually treated separately from each other.

The basics of differentiable manifolds, global calculus, differential geometry, and related topics constitute a core of information essential for the first or second year graduate student preparing for advanced courses and seminars in differential topology and geometry.

Advances in technology over the last 25 years have created a situation in which workers in diverse areas of computerscience and engineering have found it neces- sary to increase their knowledge of related fields in order to make further progress.

Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase.

Geometric measure theory has roots going back to ancient Greek mathematics, for considerations of the isoperimetric problem (to ?

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

Fuchsian reduction is a method for representing solutions of nonlinear PDEs near singularities.

Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries.

This book is an outgrowth of the special term "e;Harmonic Analysis, Representation Theory, and Integral Geometry,"e; held at the Max Planck Institute for Mathematics and the Hausdorff Research Institute for Mathematics in Bonn during the summer of 2007.

This book introduces geometric spectral theory in the context of Riemann surfaces.

This volume uses a unified approach to representation theory and automorphic forms.

Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups and probability theory.

This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics.

Riemannian Topology and Geometric Structures on Manifolds results from a similarly entitled conference held at the University of New Mexico in Albuquerque.

Hideki Omori is widely recognized as one of the world's most creative and original mathematicians.

This text presents differential forms from a geometric perspective accessible at the undergraduate level.

This monograph presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology.

The study of CR manifolds lies at the intersection of three main mathematical disciplines, partial differential equations: complex analysis in several complex variables, and differential geometry.

This research monograph is a systematic exposition of the background, methods, and recent results in the theory of cycle spaces of ?

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.