Handbook Of Differential Geometry
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Author | : Franki J.E. Dillen |
Publisher | : Elsevier |
Total Pages | : 575 |
Release | : 2005-11-29 |
Genre | : Mathematics |
ISBN | : 0080461204 |
In the series of volumes which together will constitute the "Handbook of Differential Geometry" we try to give a rather complete survey of the field of differential geometry. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent).All chapters are written by experts in the area and contain a large bibliography. In this second volume a wide range of areas in the very broad field of differential geometry is discussed, as there are Riemannian geometry, Lorentzian geometry, Finsler geometry, symplectic geometry, contact geometry, complex geometry, Lagrange geometry and the geometry of foliations. Although this does not cover the whole of differential geometry, the reader will be provided with an overview of some its most important areas.. Written by experts and covering recent research. Extensive bibliography. Dealing with a diverse range of areas. Starting from the basics
Author | : F.J.E. Dillen |
Publisher | : North Holland |
Total Pages | : 1053 |
Release | : 1999-12-30 |
Genre | : Mathematics |
ISBN | : 9780444822406 |
In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography.
Author | : F.J.E. Dillen |
Publisher | : North Holland |
Total Pages | : 1053 |
Release | : 1999-12-30 |
Genre | : Mathematics |
ISBN | : 9780444822406 |
In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography.
Author | : F.J.E. Dillen |
Publisher | : Elsevier |
Total Pages | : 1067 |
Release | : 1999-12-16 |
Genre | : Mathematics |
ISBN | : 0080532837 |
In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography.
Author | : M.K. Murray |
Publisher | : CRC Press |
Total Pages | : 292 |
Release | : 1993-04-01 |
Genre | : Mathematics |
ISBN | : 9780412398605 |
Ever since the introduction by Rao in 1945 of the Fisher information metric on a family of probability distributions, there has been interest among statisticians in the application of differential geometry to statistics. This interest has increased rapidly in the last couple of decades with the work of a large number of researchers. Until now an impediment to the spread of these ideas into the wider community of statisticians has been the lack of a suitable text introducing the modern coordinate free approach to differential geometry in a manner accessible to statisticians. Differential Geometry and Statistics aims to fill this gap. The authors bring to this book extensive research experience in differential geometry and its application to statistics. The book commences with the study of the simplest differentiable manifolds - affine spaces and their relevance to exponential families, and goes on to the general theory, the Fisher information metric, the Amari connections and asymptotics. It culminates in the theory of vector bundles, principal bundles and jets and their applications to the theory of strings - a topic presently at the cutting edge of research in statistics and differential geometry.
Author | : J.R. Sack |
Publisher | : Elsevier |
Total Pages | : 1087 |
Release | : 1999-12-13 |
Genre | : Mathematics |
ISBN | : 0080529682 |
Computational Geometry is an area that provides solutions to geometric problems which arise in applications including Geographic Information Systems, Robotics and Computer Graphics. This Handbook provides an overview of key concepts and results in Computational Geometry. It may serve as a reference and study guide to the field. Not only the most advanced methods or solutions are described, but also many alternate ways of looking at problems and how to solve them.
Author | : Shlomo Sternberg |
Publisher | : Courier Corporation |
Total Pages | : 418 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 0486292711 |
Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.
Author | : Lizhen Ji |
Publisher | : |
Total Pages | : 704 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : |
"Geometric Analysis combines differential equations with differential geometry. An important aspect of geometric analysis is to approach geometric problems by studying differential equations. Besides some known linear differential operators such as the Laplace operator, many differential equations arising from differential geometry are nonlinear. A particularly important example is the Monge-Amperè equation. Applications to geometric problems have also motivated new methods and techniques in differential equations. The field of geometric analysis is broad and has had many striking applications. This handbook of geometric analysis--the first of the two to be published in the ALM series--presents introductions and survey papers treating important topics in geometric analysis, with their applications to related fields. It can be used as a reference by graduate students and by researchers in related areas."--Back cover.
Author | : Thierry Aubin |
Publisher | : American Mathematical Soc. |
Total Pages | : 198 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 082182709X |
This textbook for second-year graduate students is intended as an introduction to differential geometry with principal emphasis on Riemannian geometry. Chapter I explains basic definitions and gives the proofs of the important theorems of Whitney and Sard. Chapter II deals with vector fields and differential forms. Chapter III addresses integration of vector fields and p-plane fields. Chapter IV develops the notion of connection on a Riemannian manifold considered as a means to define parallel transport on the manifold. The author also discusses related notions of torsion and curvature, and gives a working knowledge of the covariant derivative. Chapter V specializes on Riemannian manifolds by deducing global properties from local properties of curvature, the final goal being to determine the manifold completely. Chapter VI explores some problems in PDEs suggested by the geometry of manifolds. The author is well-known for his significant contributions to the field of geometry and PDEs - particularly for his work on the Yamabe problem - and for his expository accounts on the subject. The text contains many problems and solutions, permitting the reader to apply the theorems and to see concrete developments of the abstract theory.
Author | : David Lovelock |
Publisher | : Courier Corporation |
Total Pages | : 402 |
Release | : 2012-04-20 |
Genre | : Mathematics |
ISBN | : 048613198X |
Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.