Differential and Riemannian geometry

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

Up-to-date research in metric diffusion along compact foliations is presented in this book.

Differential and complex geometry are two central areas of mathematics with a long and intertwined history.

This book is devoted to geometric problems of foliation theory, in particular those related to extrinsic geometry, modern branch of Riemannian Geometry.

This monograph systematically explores the theory of rational maps between spheres in complex Euclidean spaces and its connections to other areas of mathematics.

This brief focuses on the structural properties of nonlinear time-delay systems.

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.

This concise textbook introduces the reader to advanced mathematical aspects of general relativity, covering topics like Penrose diagrams, causality theory, singularity theorems, the Cauchy problem for the Einstein equations, the positive mass theorem, and the laws of black hole thermodynamics.

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

The book provides an introduction of very recent results about the tensors and mainly focuses on the authors' work and perspective.

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

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 book explains and helps readers to develop geometric intuition as it relates to differential forms.

What do the classification of algebraic surfaces, Weyl's dimension formula and maximal orders in central simple algebras have in common?

This book collects papers presented in the Invited Workshop, "e;Liutex and Third Generation of Vortex Definition and Identification for Turbulence,"e; from CHAOS2020, June 9-12, 2020, which was held online as a virtual conference.

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 Czech Academy of Sciences' Institute of Information Theory and Automation.

This book aims to provide an overview of several topics in advanced differential geometry and Lie group theory, all of them stemming from mathematical problems in supersymmetric physical theories.

This book provides the latest competing research results on non-commutative harmonic analysis on homogeneous spaces with many applications.

The volume is a follow-up to the INdAM meeting "e;Special metrics and quaternionic geometry"e; held in Rome in November 2015.

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

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.

The theories of V.

A warped product manifold is a Riemannian or pseudo-Riemannian manifold whose metric tensor can be decomposed into a Cartesian product of the y geometry and the x geometry - except that the x-part is warped, that is, it is rescaled by a scalar function of the other coordinates y.

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.

This book covers recent advances in several important areas of geometric analysis including extremal eigenvalue problems, mini-max methods in minimal surfaces, CR geometry in dimension three, and the Ricci flow and Ricci limit spaces.

This book provides definitions and mathematical derivations of fundamental relationships of tensor analysis encountered in nonlinear continuum mechanics and continuum physics, with a focus on finite deformation kinematics and classical differential geometry.

This volume consists of contributions by the main participants of the 3rd International Colloquium on Differential Geometry and its Related Fields (ICDG2012), which was held in Veliko Tarnovo, Bulgaria.

In the theory of minimal submanifolds, Bernstein's problem and Plateau's problem are central topics.

Stochastic analysis on Riemannian manifolds without boundary has been well established.

Deep connections exist between harmonic and applied analysis and the diverse yet connected topics of machine learning, data analysis, and imaging science.

This book studies a category of mathematical objects called Hamiltonians, which are dependent on both time and momenta.

This book includes four courses on geometric measure theory, the calculus of variations, partial differential equations, and differential geometry.

This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology.

This volume is devoted to various aspects of Alexandrov Geometry for those wishing to get a detailed picture of the advances in the field.

Zu Recht wird Albert Einsteins Entdeckung der Allgemeinen Relativitätstheorie bewundert, denn ihre Erkenntnisse haben unseren Blick auf das Universum grundlegend verändert.

The principle aim of this unique text is to illuminate the beauty of the subject both with abstractions like proofs and mathematical text, and with visuals, such as abundant illustrations and diagrams.

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.

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.

An excellent reference for anyone needing to examine properties of harmonic vector fields to help them solve research problems.

This is the fifth volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research.

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

This contributed volume is the result of a July 2010 workshop at the University of Wuppertal Interdisciplinary Centre for Science and Technology Studies which brought together world-wide experts from physics, philosophy and history, in order to address a set of questions first posed in the 1950s: How do we compare spacetime theories?

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

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

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

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

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 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.

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