کتابهای لاتین ریاضیات علم هندسه ومکان شناسی(differential Geometry)هندسه تفاضلی


 

A Geometric Approach to Differential FormsA Geometric Approach to Differential Forms
by David Bachman - arXiv , 2003
This is a textbook on differential forms. The primary target audience is sophomore level undergraduates enrolled in a course in vector calculus. Later chapters will be of interest to advanced undergraduate and beginning graduate students.
(2934 views)

Algebraic geometry and projective differential geometryAlgebraic geometry and projective differential geometry
by Joseph M. Landsberg - arXiv , 1998
Homogeneous varieties, Topology and consequences Projective differential invariants, Varieties with degenerate Gauss images, Dual varieties, Linear systems of bounded and constant rank, Secant and tangential varieties, and more.
(3435 views)

An Introduction to Differentiable Manifolds and Riemannian GeometryAn Introduction to Differentiable Manifolds and Riemannian Geometry
by William M. Boothby - Academic Press , 1984
This is the only book available that is approachable by beginners in this subject. It is an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods.
(3948 views)

An Introduction to Gaussian GeometryAn Introduction to Gaussian Geometry
by Sigmundur Gudmundsson - Lund University , 2009
These notes introduce the beautiful theory of Gaussian geometry i.e. the theory of curves and surfaces in three dimensional Euclidean space. The text is written for students with a good understanding of linear algebra and real analysis.
(129 views)

An Introduction to Riemannian GeometryAn Introduction to Riemannian Geometry
by Sigmundur Gudmundsson - Lund University , 2010
The main purpose of these lecture notes is to introduce the beautiful theory of Riemannian Geometry. Of special interest are the classical Lie groups allowing concrete calculations of many of the abstract notions on the menu.
(2431 views)

Combinatorial Geometry with Application to Field TheoryCombinatorial Geometry with Application to Field Theory
by Linfan Mao - InfoQuest , 2009
Topics covered in this book include fundamental of mathematical combinatorics, differential Smarandache n-manifolds, combinatorial or differentiable manifolds and submanifolds, Lie multi-groups, combinatorial principal fiber bundles, etc.
(580 views)

Complex Analysis on Riemann SurfacesComplex Analysis on Riemann Surfaces
by Curtis McMullen - Harvard University , 2005
Contents: Maps between Riemann surfaces; Sheaves and analytic continuation; Algebraic functions; Holomorphic and harmonic forms; Cohomology of sheaves; Cohomology on a Riemann surface; Riemann-Roch; Serre duality; Maps to projective space; etc.
(1429 views)

Complex Analytic and Differential GeometryComplex Analytic and Differential Geometry
by Jean-Pierre Demailly - Universite de Grenoble , 2007
Basic concepts of complex geometry, coherent sheaves and complex analytic spaces, positive currents and potential theory, sheaf cohomology and spectral sequences, Hermitian vector bundles, Hodge theory, positive vector bundles, etc.
(3689 views)

Complex Geometry of Nature and General RelativityComplex Geometry of Nature and General Relativity
by Giampiero Esposito - arXiv , 1999
An attempt is made of giving a self-contained introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, spinor and twistor methods, heaven spaces.
(3060 views)

Complex Manifolds and Hermitian Differential GeometryComplex Manifolds and Hermitian Differential Geometry
by Andrew D. Hwang - University of Toronto , 1997
The intent is not to give a thorough treatment of the algebraic and differential geometry of complex manifolds, but to introduce the reader to material of current interest as quickly as possible. A number of interesting examples is provided.
(169 views)

Constrained Mechanics and Lie TheoryConstrained Mechanics and Lie Theory
by Robert Hermann - Math Sci Press , 1992
In this volume, the author pushes along the road of integrating Mechanics and Control with the insights deriving from Lie, Cartan, Ehresmann, and Spencer. The author looks at the Pure and Applied worlds in an integrated way.
(157 views)

Course of Differential GeometryCourse of Differential Geometry
by Ruslan Sharipov - Samizdat Press , 2004
Textbook for the first course of differential geometry. It covers the theory of curves in three-dimensional Euclidean space, the vectorial analysis both in Cartesian and curvilinear coordinates, and the theory of surfaces in the space E.
(2766 views)

Cusps of Gauss MappingsCusps of Gauss Mappings
by Thomas Banchoff, Terence Gaffney, Clint McCrory - Pitman Advanced Pub. Program , 1982
Gauss mappings of plane curves, Gauss mappings of surfaces, characterizations of Gaussian cusps, singularities of families of mappings, projections to lines, focal and parallel surfaces, projections to planes, singularities and extrinsic geometry.
(1923 views)

Differentiable ManifoldsDifferentiable Manifolds
by Nigel Hitchin , 2003
The historical driving force of the theory of manifolds was General Relativity, where the manifold is four-dimensional spacetime, wormholes and all. This text is occupied with the theory of differential forms and the exterior derivative.
(4003 views)

Differential Geometry Course NotesDifferential Geometry Course Notes
by Richard Koch - University of Oregon , 2005
These are differential geometry course notes. From the table of contents: Preface; Curves; Surfaces; Extrinsic Theory; The Covariant Derivative; The Theorema Egregium; The Gauss-Bonnet Theorem; Riemann's Counting Argument.
(189 views)

Differential Geometry in PhysicsDifferential Geometry in Physics
by Gabriel Lugo - University of North Carolina at Wilmington , 2006
These notes were developed as a supplement to a course on Differential Geometry at the advanced undergraduate level, which the author has taught. This texts has an early introduction to differential forms and their applications to Physics.
(3477 views)

Differential Geometry: A First Course in Curves and SurfacesDifferential Geometry: A First Course in Curves and Surfaces
by Theodore Shifrin - University of Georgia , 2010
Contents: Arclength Parametrization; Local Theory: Frenet Frame; Parametrized Surfaces and the First Fundamental Form; The Gauss Map and the Second Fundamental Form; Covariant Differentiation, Parallel Translation, and Geodesics; etc.
(389 views)

Elementary Differential GeometryElementary Differential Geometry
by Gilbert Weinstein - UAB , 2009
These notes are for a beginning graduate level course in differential geometry. It is assumed that this is the students' first course in the subject. Thus the choice of subjects and presentation has been made to facilitate a concrete picture.
(321 views)

Exterior Differential Systems and Euler-Lagrange Partial Differential EquationsExterior Differential Systems and Euler-Lagrange Partial Differential Equations
by Robert L. Bryant, Phillip A. Griffiths, Daniel A. Grossman - University Of Chicago Press , 2008
The authors present the results of their development of a theory of the geometry of differential equations, focusing especially on Lagrangians and Poincare-Cartan forms. They also cover certain aspects of the theory of exterior differential systems.
(3236 views)

Foundations of Differential GeometryFoundations of Differential Geometry
by Peter W. Michor - Universitat Wien , 1997
Contents: Differentiable Manifolds; Submersions and Immersions; Vector Fields and Flows; Lie Groups; Vector Bundles; Differential Forms; Integration on Manifolds; De Rham cohomology; Cohomology with compact supports and Poincare duality; etc.
(78 views)

Functional Differential GeometryFunctional Differential Geometry
by Gerald Jay Sussman, Jack Wisdom - MIT , 2005
Differential geometry is deceptively simple. It is surprisingly easy to get the right answer with informal symbol manipulation. We use computer programs to communicate a precise understanding of the computations in differential geometry.
(262 views)

Introduction to Differential Geometry and General RelativityIntroduction to Differential Geometry and General Relativity
by Stefan Waner , 2005
Smooth manifolds and scalar fields, tangent vectors, contravariant and covariant vector fields, tensor fields, Riemannian manifolds, locally Minkowskian manifolds, covariant differentiation, the Riemann curvature tensor, premises of general relativity.
(4300 views)

Introduction to Homological GeometryIntroduction to Homological Geometry
by Martin A. Guest - arXiv , 2001
This is an introduction to some of the analytic aspects of quantum cohomology. The small quantum cohomology algebra, regarded as an example of a Frobenius manifold, is described without going into the technicalities of a rigorous definition.
(131 views)

Introduction to Lie Groups, Adjoint Action and Some GeneralizationsIntroduction to Lie Groups, Adjoint Action and Some Generalizations
by Marcos M. Alexandrino, Renato G. Bettiol - arXiv , 2009
These lecture notes provide a concise introduction to Lie groups, Lie algebras, and isometric and adjoint actions, aiming at advanced undergraduate and graduate students. A special focus is given to maximal tori and roots of compact Lie groups.
(366 views)

Introduction to Symplectic and Hamiltonian GeometryIntroduction to Symplectic and Hamiltonian Geometry
by Ana Cannas da Silva , 2007
The text covers foundations of symplectic geometry in a modern language. It describes symplectic manifolds and their transformations, and explains connections to topology and other geometries. It also covers hamiltonian fields and hamiltonian actions.
(1904 views)

Lectures on Symplectic GeometryLectures on Symplectic Geometry
by Ana Cannas da Silva - Springer , 2006
An introduction to symplectic geometry and topology, it provides a useful and effective synopsis of the basics of symplectic geometry and serves as the springboard for a prospective researcher. The text is written in a clear, easy-to-follow style.
(2355 views)

Natural Operations in Differential GeometryNatural Operations in Differential Geometry
by Ivan Kolar, Peter W. Michor, Jan Slovak - Springer , 1993
A comprehensive textbook on all basic structures from the theory of jets. It begins with an introduction to differential geometry. After reduction each problem to a finite order setting, the remaining discussion is based on properties of jet spaces.
(2129 views)

Notes on Differential GeometryNotes on Differential Geometry
by Noel J. Hicks - Van Nostrand , 1965
A concise introduction to differential geometry. The ten chapters of Hicks' book contain most of the mathematics that has become the standard background for not only differential geometry, but also much of modern theoretical physics and cosmology.
(312 views)

Notes on Differential Geometry and Lie GroupsNotes on Differential Geometry and Lie Groups
by Jean Gallier - University of Pennsylvania , 2010
Contents: Introduction to Manifolds and Lie Groups; Review of Groups and Group Actions; Manifolds; Construction of Manifolds From Gluing Data; Lie Groups, Lie Algebra, Exponential Map; The Derivative of exp and Dynkin's Formula; etc.
(315 views)

Probability, Geometry and Integrable SystemsProbability, Geometry and Integrable Systems
by Mark Pinsky, Bjorn Birnir - Cambridge University Press , 2007
The three main themes of this book are probability theory, differential geometry, and the theory of integrable systems. The papers included here demonstrate a wide variety of techniques that have been developed to solve various mathematical problems.
(2755 views)

Projective and Polar SpacesProjective and Polar Spaces
by Peter J. Cameron - Queen Mary College , 1991
The author is concerned with the geometry of incidence of points and lines, over an arbitrary field, and unencumbered by metrics or continuity (or even betweenness). The treatment of these themes blends the descriptive with the axiomatic.
(1648 views)

Projective Differential Geometry Old and NewProjective Differential Geometry Old and New
by V. Ovsienko, S. Tabachnikov - Cambridge University Press , 2004
This book provides a route for graduate students and researchers to contemplate the frontiers of contemporary research in projective geometry. The authors include exercises and historical comments relating the basic ideas to a broader context.
(2098 views)

Riemann Surfaces, Dynamics and GeometryRiemann Surfaces, Dynamics and Geometry
by Curtis McMullen - Harvard University , 2008
This course will concern the interaction between: hyperbolic geometry in dimensions 2 and 3, the dynamics of iterated rational maps, and the theory of Riemann surfaces and their deformations. Intended for advanced graduate students.
(1895 views)

Symplectic GeometrySymplectic Geometry
by Ana Cannas da Silva - Princeton University , 2004
An overview of symplectic geometry – the geometry of symplectic manifolds. From a language of classical mechanics, symplectic geometry became a central branch of differential geometry and topology. This survey gives a partial flavor on this field.
(1903 views)

Synthetic Differential GeometrySynthetic Differential Geometry
by Anders Kock - Cambridge University Press , 2006
Synthetic differential geometry is a method of reasoning in differential geometry and calculus. This book is the second edition of Anders Kock's classical text, many notes have been included commenting on new developments.
(2193 views)

The Convenient Setting of Global AnalysisThe Convenient Setting of Global Analysis
by Andreas Kriegl, Peter W. Michor - American Mathematical Society , 1997
This book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory.
(1920 views)

Tight and Taut SubmanifoldsTight and Taut Submanifolds
by Thomas E. Cecil, Shiing-shen Chern - Cambridge University Press , 1997
Tight and taut submanifolds form an important class of manifolds with special curvature properties, one that has been studied intensively by differential geometers since the 1950's. This book contains six articles by leading experts in the field.
(629 views)

Topics in Differential GeometryTopics in Differential Geometry
by Peter W. Michor - American Mathematical Society , 2008
Fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry.
(336 views)