Differential and Riemannian geometry

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.

Das vorliegende Lehrbuch bietet eine moderne Einführung in die Differentialgeometrie etwa im Umfang einer einsemestrigen Vorlesung.

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

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

This volume gathers contributions reflecting topics presented during an INDAM workshop held in Rome in May 2016.

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 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.

INTRODUCTION TO DIFFERENTIAL GEOMETRY WITH TENSOR APPLICATIONS This is the only volume of its kind to explain, in precise and easy-to-understand language, the fundamentals of tensors and their applications in differential geometry and analytical mechanics with examples for practical applications and questions for use in a course setting.

A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature.

Soviet citizens can buy Monastyrsky's biography of Riemann for eleven kopeks.

INTRODUCTION TO DIFFERENTIAL GEOMETRY WITH TENSOR APPLICATIONS This is the only volume of its kind to explain, in precise and easy-to-understand language, the fundamentals of tensors and their applications in differential geometry and analytical mechanics with examples for practical applications and questions for use in a course setting.

After several decades of reduced contact, the interaction between physicists and mathematicians in the front-line research of both fields recently became deep and fruit- ful again.

This volume originated in talks given in Cortona at the conference "e;Geometric aspects of harmonic analysis"e; held in honor of the 70th birthday of Fulvio Ricci.

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

This book illustrates the deep roots of the geometrically nonlinear kinematics ofgeneralized continuum mechanics in differential geometry.

This is the first comprehensive book on information geometry, written by the founder of the field.

This book is based upon my monograph Index Theory for Hamiltonian Systems with Applications published in 1993 in Chinese, and my notes for lectures and courses given at Nankai University, Brigham Young University, ICTP-Trieste, and the Institute of Mathematics of Academia Sinica during the last ten years.

Riemannian Topology and Geometric Structures on Manifolds results from a similarly entitled conference held at the University of New Mexico in Albuquerque.

The aim of this book is to facilitate the use of Stokes' Theorem in applications.

This book contains papers given at the International Singularity Conference held in 1991 at Lille.

This book is an exposition of "e;Singular Semi-Riemannian Geometry"e;- the study of a smooth manifold furnished with a degenerate (singular) metric tensor of arbitrary signature.

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

This book provides a concrete description of the identity connected components of the real and complex exceptional Lie groups.

This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three.

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Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors.

The topics in this survey volume concern research done on the differential geom- etry of foliations over the last few years.

This book pedagogically describes recent developments in gauge theory, in particular four-dimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation theory, vertex operator algebras.

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 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.

This monograph provides some useful tools for performing global geometric analysis on real analytic manifolds.

In this volume are collected notes of lectures delivered at the First In- ternational Research Institute of the Mathematical Society of Japan.

The book is designed chiefly for the use of students and teachers.

The implicit function theorem is part of the bedrock of mathematical analysis and geometry.

Provides the first systematic study of geometry and topology of locally symmetric rank one manifolds and dynamics of discrete action of their fundamental groups.

Minimal Surfaces I is an introduction to the field of minimal surfaces and a presentation of the classical theory as well as of parts of the modern development centered around boundary value problems.

Astronomers do not do experiments.

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 proceedings volume gathers selected, revised papers presented at the X International Meeting on Lorentzian Geometry (GeLoCor 2021), virtually held at the University of Cordoba, Spain, on February 1-5, 2021.

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

Many branches of science and engineering involve applications of mathematical analysis.