Differential and Riemannian geometry

This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing.

This textbook offers an introduction to differential geometry designed for readers interested in modern geometry processing.

This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics.

This textbook offers readers a self-contained introduction to quantitative Tamarkin category theory.

This book provides an introduction to some aspects of the flourishing field of nonsmooth geometric analysis.

This is a volume originating from the Conference on Partial Differential Equations and Applications, which was held in Moscow in November 2018 in memory of professor Boris Sternin and attracted more than a hundred participants from eighteen countries.

This book is an introduction to the theory of quasiconformal and quasiregular mappings in the euclidean n-dimensional space, (where n is greater than 2).

This book presents a step-by-step guide to the basic theory of multivectors and spinors, with a focus on conveying to the reader the geometric understanding of these abstract objects.

This book provides a comprehensive account of a modern generalisation of differential geometry in which coordinates need not commute.

This book aims to provide a friendly introduction to non-commutative geometry.

This book provides an introduction to the mathematics and physics of general relativity, its basic physical concepts, its observational implications, and the new insights obtained into the nature of space-time and the structure of the universe.

This unique textbook offers a mathematically rigorous presentation of the theory of relativity, emphasizing the need for a critical analysis of the foundations of general relativity in order to best study the theory and its implications.

Collecting together the lecture notes of the CIME Summer School held in Cetraro in July 2018, the aim of the book is to introduce a vast range of techniques which are useful in the investigation of complex manifolds.

This proceedings is based on the interdisciplinary workshop held in Madrid, 5-9 March 2018, dedicated to Alberto Ibort on his 60th birthday.

This updated and expanded edition presents a highly accurate specification for part surface machining.

This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical.

This book provides a complete exposition of equidistribution and counting problems weighted by a potential function of common perpendicular geodesics in negatively curved manifolds and simplicial trees.

The book describes how curvature measures can be introduced for certain classes of sets with singularities in Euclidean spaces.

This book provides an up-to-date presentation of homogeneous pseudo-Riemannian structures, an essential tool in the study of pseudo-Riemannian homogeneous spaces.

This volume presents lectures given at the Summer School Wisla 18: Nonlinear PDEs, Their Geometry, and Applications, which took place from August 20 - 30th, 2018 in Wisla, Poland, and was organized by the Baltic Institute of Mathematics.

This textbook provides a coherent, integrated look at various topics from undergraduate analysis.

This book treats the two-dimensional non-linear supersymmetric sigma model or spinning string from the perspective of supergeometry.

This book explains the foundations of holomorphic curve theory in contact geometry.

This book collects independent contributions on current developments in quantum information theory, a very interdisciplinary field at the intersection of physics, computer science and mathematics.

Aimed toward graduate students and research mathematicians, with minimal prerequisites this book  provides a fresh take on Alexandrov geometry and explains the importance of CAT(0) geometry in geometric group theory.

This book develops a novel approach to perturbative quantum field theory: starting with a perturbative formulation of classical field theory, quantization is achieved by means of deformation quantization of the underlying free theory and by applying the principle that as much of the classical structure as possible should be maintained.

This is the first comprehensive monograph to thoroughly investigate constant width bodies, which is a classic area of interest within convex geometry.

This volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928 - February 2, 2017), is a collection of 19 invited papers by leading mathematicians working in Lie theory, representation theory, algebra, geometry, and mathematical physics.

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 develops a spectral theory for the integrable system of 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation.

This book consists of two lecture notes on geometric flow equations (O.

This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical.

This book presents problems and solutions in calculus with curvilinear coordinates.

This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing.

The 2nd edition of this textbook features more than 100 pages of new material, including four new chapters, as well as an improved discussion of differential geometry concepts and their applications.

A-infinity structure was introduced by Stasheff in the 1960s in his homotopy characterization of based loop space, which was the culmination of earlier works of Sugawara's homotopy characterization of H-spaces and loop spaces.

This invaluable book, based on the many years of teaching experience of both authors, introduces the reader to the basic ideas in differential topology.

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.

This book presents a new front of research in conformal geometry, on sign-changing Yamabe-type problems and contact form geometry in particular.

A central area of study in Differential Geometry is the examination of the relationship between the purely algebraic properties of the Riemann curvature tensor and the underlying geometric properties of the manifold.

The book presents a comprehensive guide to the study of Lie systems from the fundamentals of differential geometry to the development of contemporary research topics.

In view of the significance of the array manifold in array processing and array communications, the role of differential geometry as an analytical tool cannot be overemphasized.

Enumerative geometry is a core area of algebraic geometry that dates back to Apollonius in the second century BCE.

This book is an introductory text on Differential Geometry presented in tensorial approach.

Several important problems arising in Physics, Differential Geometry and other topics lead to consider semilinear variational equations of strongly indefinite type and a great deal of work has been devoted to their study.

This book provides General Relativity problems to be tackled both analytically and symbolically-numerically with the Mathematica software.

This book provides a systematic presentation of the mathematical foundation of modern physics with applications particularly within classical mechanics and the theory of relativity.

This book is the first monograph dedicated entirely to Willmore energy and Willmore surfaces as contemporary topics in differential geometry.

A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing shows how to use a collection of mathematical techniques to solve important problems in applied mathematics and computer science areas.

This book provides a comprehensive introduction to Submanifold theory, focusing on general properties of isometric and conformal immersions of Riemannian manifolds into space forms.