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.
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.
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 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.
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.
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.
This volume resulted from presentations given at the international "e;Brainstorming Workshop on New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series"e;, that took place at the Instituto de Ciencias Matematicas (ICMAT) in Madrid, Spain.
This book, Differential Geometry: Riemannian Geometry and Isometric Immersions (Book I-B), is the second in a captivating series of four books presenting a choice of topics, among fundamental and more advanced in differential geometry (DG).
This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three.
Fractal Functions, Fractal Surfaces, and Wavelets, Second Edition, is the first systematic exposition of the theory of local iterated function systems, local fractal functions and fractal surfaces, and their connections to wavelets and wavelet sets.
This book is a self-contained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by non-overdetermining data of solutions.
The basic goals of the book are: (i) to introduce the subject to those interested in discovering it, (ii) to coherently present a number of basic techniques and results, currently used in the subject, to those working in it, and (iii) to present some of the results that are attractive in their own right, and which lend themselves to a presentation not overburdened with technical machinery.
This book consists of five chapters presenting problems of current research in mathematics, with its history and development, current state, and possible future direction.
This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature.
In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given.
Written primarily for students who have completed the standard first courses in calculus and linear algebra, Elementary Differential Geometry, Revised 2nd Edition, provides an introduction to the geometry of curves and surfaces.
After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry.
In the series of volumes which together will constitute the "e;Handbook of Differential Geometry"e; we try to give a rather complete survey of the field of differential geometry.
This book presents a multidisciplinary guide to gauge theory and gravity, with chapters by the world's leading theoretical physicists, mathematicians, historians and philosophers of science.
