This book offers an overview of selected topics on the topology of singularities, with emphasis on its relations to other branches of geometry and topology.
This is the fifth and revised edition of a well-received textbook that aims at bridging the gap between the engineering course of tensor algebra on the one hand and the mathematical course of classical linear algebra on the other hand.
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.
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.
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 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 book describes about unlike usual differential dynamics common in mathematical physics, heterogenesis is based on the assemblage of differential constraints that are different from point to point.
Focussing on the mathematics related to the recent proof of ergodicity of the (Weil-Petersson) geodesic flow on a nonpositively curved space whose points are negatively curved metrics on surfaces, this book provides a broad introduction to an important current area of research.
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 volume explores the interplay between mathematical and physical research and the interactions of twentieth-century scientists within their academic communities.
This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Bedlewo, Poland in September 2015.
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 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 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 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.
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.
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.
Deep connections exist between harmonic and applied analysis and the diverse yet connected topics of machine learning, data analysis, and imaging science.
