Differential and Riemannian geometry

A thoroughly revised introduction to non-commutative geometry.

In the last decade several international conferences on Finsler, Lagrange and Hamilton geometries were organized in Braov, Romania (1994), Seattle, USA (1995), Edmonton, Canada (1998), besides the Seminars that periodically are held in Japan and Romania.

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.

The totality of the eigenvalues of the Laplacian of a compact Riemannian manifold is called the spectrum.

This textbook offers a different approach to classical textbooks in Differential Geometry.

Shows novel and modern ways of solving differential equations using methods from contact and symplectic geometry.

A new approach to studying Fréchet geometry using projective limits of geometrical objects modelled on Banach spaces.

An up-to-date survey of research in singularity theory.

um das zur Lösung konkreter geometrischer Einzelfragen nötige Rüstzeug zu ver­ mitteln, ist auch stets die koordinatenmäßige Behandlung berücksichtigt.

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.

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Shiing-Shen Chern (1911-2004) was one of the leading differential geometers of the twentieth century.

Differential geometry is a mathematical discipline that uses the techniques of differential calculus and integral calculus, as well as linear algebra and multilinear algebra, to study problems in geometry.

Gaussian scale-space is one of the best understood multi-resolution techniques available to the computer vision and image analysis community.

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

In recent years, the study of the Monge-Ampere equation has received consider- able attention and there have been many important advances.

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 book is an outgrowth of the activities of the Center for Geometry and Mathematical Physics (CGMP) at Penn State from 1996 to 1998.

This book is a collection of selected research papers, some of which were presented at the International Conference on Differential Geometry, Algebra and Analysis (ICDGAA 2016), held at the Department of Mathematics, Jamia Millia Islamia, New Delhi, from 15-17 November 2016.

This is a monograph on geometrical and topological features which arise in quantum field theory.

The aim of these lecture notes is to give an essentially self-contained introduction to the basic regularity theory for energy minimizing maps, including recent developments concerning the structure of the singular set and asymptotics on approach to the singular set.

This monograph presents the geometric foundations of continuum mechanics.

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 is the second edition of this best selling problem book for students, now containing over 400 completely solved exercises on differentiable manifolds, Lie theory, fibre bundles and Riemannian manifolds.

This book provides an upto date information on metric, connection and curva- ture symmetries used in geometry and physics.

Geometric dynamics is a tool for developing a mathematical representation of real world phenomena, based on the notion of a field line described in two ways: -as the solution of any Cauchy problem associated to a first-order autonomous differential system; -as the solution of a certain Cauchy problem associated to a second-order conservative prolongation of the initial system.

This book provides detailed information on index theories and their applications, especially Maslov-type index theories and their iteration theories for non-periodic solutions of Hamiltonian systems.

This book features chapters written by renowned scientists from various parts of the world, providing an up-to-date survey of submanifold theory, spanning diverse topics and applications.

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

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 monograph presents the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometry.

This book is a collection of papers in memory of Gu Chaohao on the subjects of Differential Geometry, Partial Differential Equations and Mathematical Physics that Gu Chaohao made great contributions to with all his intelligence during his lifetime.

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Physics and mathematics students are as eager as ever to become acquainted withthefoundationsofgeneralrelativityandsomeofitsmajorapplicationsin astrophysics and cosmology.

In this second edition, the main additions are a section devoted to surfaces with constant negative curvature, and an introduction to conformal geometry.

This book illustrates the broad range of Jerry Marsden's mathematical legacy in areas of geometry, mechanics, and dynamics, from very pure mathematics to very applied, but always with a geometric perspective.

This volume presents modern developments in analysis, PDEs and geometric analysis by some of the leading worldwide experts, prominent junior and senior researchers who were invited to be part of the Ghent Analysis & PDE Center Methusalem Seminars from 2021 to 2022.

Intended for a one year course, this text serves as a single source, introducing readers 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.

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 volume presents lectures given at the Wisla 19 Summer School: Differential Geometry, Differential Equations, and Mathematical Physics, which took place from August 19 - 29th, 2019 in Wisla, Poland, and was organized by the Baltic Institute of Mathematics.

The focus of this book is on providing students with insights into geometry that can help them understand deep learning from a unified perspective.

Foliations, groups and pseudogroups are objects which are closely related via the notion of holonomy.