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Riemannian Geometry
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by
Manfredo P Do Carmo, Francis Flaherty (Translator)
Publicationes Mathematicae "In the reviewer's opinion, this is a superb book which makes learning a real pleasure." - Revue Romaine de Mathematiques Pures et Appliquees "This main-stream presentation of differential geometry serves well for a course on Riemannian geometry, and it is complemented by many annotated exercises." - Monatshefte F. ...
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Riemannian Geometry
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by
Peter Petersen
This book is intended for a one year course in Riemannian Geometry. It will serve as a single source, introducing students 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. Instead of variational techniques, the author uses a ...
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Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings
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Michel L Lapidus, Machiel Van Frankenhuysen
Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings. Complex dimensions of a fractal string, defined as ...
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Riemannian geometry a modern introduction
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by
Chavel
This title provides an introduction to the geometry of curved spaces. Its main theme is the effect of the curvature of these spaces on the usual notions of geometry: angles, lengths, areas, and volumes; and those new notions and ideas motivated by curvature itself. A number of completely new themes are created by curvature: they include local ...
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The Theory of Spinors
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Elie Cartan
Describes orthgonal and related Lie groups, using real or complex parameters and indefinite metrics. Develops theory of spinors by giving a purely geometric definition of these mathematical entities.
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Differential Geometry and Relativity Theory: An Introduction
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Richard L Faber
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Riemannian Geometry of Contact and Symplectic Manifolds
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by
David E Blair
This monograph deals with the Riemannian geometry of both symplectic and contact manifolds, with particular emphasis on the latter. The text is carefully presented. Topics unfold systematically from Chapter 1, which examines the general theory of symplectic manifolds. Principal circle bundles (Chapter 2) are then discussed as a prelude to the ...
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Comparison Geometry
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Karsten Grove (Editor), Peter Petersen (Editor)
This book documents the focus on a branch of Riemannian geometry called Comparison Geometry. The simple idea of comparing the geometry of an arbitrary Riemannian manifold with the geometries of constant curvature spaces has seen a tremendous evolution of late. This volume is an up-to-date reflection of the recent development regarding spaces with ...
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Flow Lines and Algebraic Invariants in Contact Form Geometry
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by
Abbas Bahri
This text features a careful treatment of flow lines and algebraic invariants in contact form geometry, a vast area of research connected to symplectic field theory, pseudo-holomorphic curves, and Gromov-Witten invariants (contact homology). In particular, this work develops a novel algebraic tool in this field: rooted in the concept of critical ...
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Some Nonlinear Problems in Riemannian Geometry
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by
Thierry Aubin
During the last few years, the field of nonlinear problems has undergone great development. This book consisting of the updated Grundlehren volume 252 by the author and of a newly written part, deals with some important geometric problems that are of interest to many mathematicians and scientists but have only recently been partially solved. Each ...
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A Sampler of Riemann-Finsler Geometry
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David Bao (Editor), Robert L Bryant (Editor), Silvio Levy (Editor)
Finsler geometry generalises Riemannian geometry in the same sense that Banach spaces generalise Hilbert spaces. This book presents an expository account of seven important topics in Riemann--Finsler geometry, ones which have recently undergone significant development but have not had a detailed pedagogical treatment elsewhere. Each article will ...
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Explorations in Complex and Riemannian Geometry: A Volume Dedicated to Robert E. Greene
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by
Robert Everist Greene
This book contains contributions by an impressive list of leading mathematicians. The articles include high-level survey and research papers exploring contemporary issues in geometric analysis, differential geometry, and several complex variables. Many of the articles will provide graduate students with a good entry point into important areas of ...
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Einstein Manifolds
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by
A L Besse
Einstein's equations stem from General Relativity. In the context of Riemannian manifolds, an independent mathematical theory has developed around them. Recently, it has produced several striking results, which have been of great interest also to physicists. This Ergebnisse volume is the first book which presents an up-to-date overview of the ...
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Blow-Up Theory for Elliptic Pdes in Riemannian Geometry (MN-45)
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by
Olivier Druet, Emmanuel Hebey, Frederic Robert
Elliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis, geometry, and physics. The equations studied here are of the well-known Yamabe type. They involve Schrodinger operators on the left hand side and a critical nonlinearity on the right hand ...
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Riemannian Geometry: A Beginner's Guide
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by
Frank Morgan
The author establishes basic material early to describe the most important geometric features of curved objects from the plebian racetrack to the grand structures of the universe. The text concludes with a discussion of global geometry and current research on energy minimizing curves.
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The Geometry of Total Curvature on Complete Open Surfaces
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by
Katsuhiro Shiohama, Takashi Shioya, Minoru Tanaka
This is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, though their work, much of which has never appeared in book ...
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Riemannian Geometry, Geometric Analysis
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by
Jurgen Jost
This text on Riemannian geometry and geometric analysis is written for graduates and reseachers and includes material new to the late 1990s on Ginzburg-Landau, Seibert-Witten functionals, spin geometry and Dirac operators.
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Spectral Geometry, Riemannian Submersions, and the Gromov-Lawson Conjecture
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Peter B Gilkey, John V Leahy, Jeonghyeong Park
This cutting-edge, standard-setting text explores the spectral geometry of Riemannian submersions. Working for the most part with the form valued Laplacian in the class of smooth compact manifolds without boundary, the authors study the relationship-if any-between the spectrum of Dp on Y and Dp on Z, given that Dp is the p form valued Laplacian ...
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Geometry IV: Non-Regular Riemannian Geometry
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by
Yu G Reshetnyak (Contributions by), E Primrose (Translator), V N Berestovskij (Contributions by)
This volume of the Encyclopaedia contains two articles,which give a survey of modern research into non-regularRiemannian geometry, carried out mostly by Russianmathematicians.The first article written by Reshetnyak is devoted to thetheory of two-dimensional Riemannian manifolds of boundedcurvature. Concepts of Riemannian geometry, such as the ...
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Beyond Geometry: Classic Papers from Riemann to Einstein
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Peter Pesic (Editor)
Eight essays trace seminal ideas about the foundations of geometry that led to the development of Einstein's general theory of relativity. This is the only English-language collection of these important papers, some of which are extremely hard to find. Contributors include Helmholtz, Klein, Clifford, Poincare, and Cartan.
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Curvature and Homology
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by
Samuel I Goldberg
Thorough treatment of specialized branch of differential geometry. Covers Riemannian manifolds, topology of differentiable manifolds, compact Lie groups, other topics. Exercises.
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Riemannian Geometry
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by
T J Willmore
The subject of differential geometry has developed so extensively since T.J. Willmore's book "Introduction to Differential Geometry" appeared over 30 years ago, that a new book with particular emphasis on recent work in Riemannian geometry was necessary. The methods used include classical tensor calculus, the suffix-free calculus and the method of ...
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Riemannian Geometry During the Second Half of the Twentieth Century
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by
Marcel Berger
During its first hundred years, Riemannian geometry enjoyed steady, but undistinguished growth as a field of mathematics. In the last fifty years of the twentieth century, however, it has exploded with activity. Berger marks the start of this period with Rauch's pioneering paper of 1951, which contains the first real pinching theorem and an ...
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An Introduction to Riemann-Finsler Geometry
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by
David Dai-Wai Bao, Zhongmin Shen, Shiing-Shen Chern
In Riemannian geometry, measurements are made with both yardsticks and protractors. These tools are represented by a family of inner-products. In Riemann-Finsler geometry (or Finsler geometry for short), one is in principle equipped with only a family of Minkowski norms. So yardsticks are assigned but protractors are not. With such a limited tool ...
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The Riemann Legacy: Riemannian Ideas in Mathematics and Physics
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by
Krzysztof Maurin
This is a study of Riemannian ideas and their descendants. Riemann (1826-1866) perceived mathematics and physics as one discipline and thought of himself as both mathematician and physicist. The book should be useful to those interested in such diverse fields as the mathematics of physics, algebra and number theory, topology and geometry, analysis ...
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