 # Differential Geometry

## e-books in Differential Geometry category Projective Differential Geometry Of Curves And Surfaces
by - The University Of Chicago Press ,
Projective Differential Geometry is largely a product of the first three decades of the twentieth century. The theory has been developed in five or more different languages, by three or four well-recognized methods, in various and sundry notations.
(2214 views) Manifolds: Current Research Areas
by - InTech ,
Differential geometry is a very active field of research and has many applications to areas such as physics and gravity, for example. The papers in this book cover a number of subjects which will be of interest to workers in these areas.
(2491 views) Advances in Discrete Differential Geometry
by - Springer ,
This is the book on a newly emerging field of discrete differential geometry. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics.
(3686 views) Principles of Differential Geometry
by - viXra ,
A collection of notes about differential geometry prepared as part of tutorials about topics and applications related to tensor calculus. They can be used as a reference for a first course on the subject or as part of a course on tensor calculus.
(2921 views) Exterior Differential Systems
by - MSRI ,
An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. This book gives a treatment of exterior differential systems. It includes both the theory and applications.
(2987 views) Triangles, Rotation, a Theorem and the Jackpot
by - arXiv ,
This paper introduced undergraduates to the Atiyah-Singer index theorem. It includes a statement of the theorem, an outline of the easy part of the heat equation proof. It includes counting lattice points and knot concordance as applications.
(5748 views) Lectures on Minimal Surface Theory
by - arXiv ,
The goal was to give beginning graduate students an introduction to some of the most important basic facts and ideas in minimal surface theory. Prerequisites: the reader should know basic complex analysis and elementary differential geometry.
(5086 views) Noncompact Harmonic Manifolds
by - arXiv ,
We provide a survey on recent results on noncompact simply connected harmonic manifolds, and we also prove many new results, both for general noncompact harmonic manifolds and for noncompact harmonic manifolds with purely exponential volume growth.
(4297 views) Notes on Symmetric Spaces
by - arXiv ,
Contents: Affine connections and transformations; Symmetric spaces; Orthogonal symmetric Lie algebras; Examples; Noncompact symmetric spaces; Compact semisimple Lie groups; Hermitian symmetric spaces; Classification of real simple Lie algebras.
(5060 views) Geometric Wave Equations
by - arXiv ,
We discuss the solution theory of geometric wave equations as they arise in Lorentzian geometry: for a normally hyperbolic differential operator the existence and uniqueness properties of Green functions and Green operators is discussed.
(6467 views) Introduction to Evolution Equations in Geometry
by - arXiv ,
The author aimed at providing a first introduction to the main general ideas on the study of the Ricci flow, as well as guiding the reader through the steps of Kaehler geometry for the understanding of the complex version of the Ricci flow.
(6206 views) Gauge Theory for Fiber Bundles
by - Universitaet Wien ,
Gauge theory usually investigates the space of principal connections on a principal fiber bundle (P,p,M,G) and its orbit space under the action of the gauge group (called the moduli space), which is the group of all principal bundle automorphisms...
(5753 views) Orthonormal Basis in Minkowski Space
by - arXiv ,
In this paper, we considered the definition of orthonormal basis in Minkowski space, the structure of metric tensor relative to orthonormal basis, procedure of orthogonalization. Contents: Preface; Minkowski Space; Examples of Minkowski Space.
(6549 views) Lectures on Fibre Bundles and Differential Geometry
by - Tata Institute of Fundamental Research ,
From the table of contents: Differential Calculus; Differentiable Bundles; Connections on Principal Bundles; Holonomy Groups; Vector Bundles and Derivation Laws; Holomorphic Connections (Complex vector bundles, Almost complex manifolds, etc.).
(6766 views) Synthetic Geometry of Manifolds
by - University of Aarhus ,
This textbook can be used as a non-technical and geometric gateway to many aspects of differential geometry. The audience of the book is anybody with a reasonable mathematical maturity, who wants to learn some differential geometry.
(7227 views) Ricci-Hamilton Flow on Surfaces
by - Tsinghua University ,
Contents: Ricci-Hamilton flow on surfaces; Bartz-Struwe-Ye estimate; Hamilton's another proof on S2; Perelman's W-functional and its applications; Ricci-Hamilton flow on Riemannian manifolds; Maximum principles; Curve shortening flow on manifolds.
(6266 views) Lectures on Exterior Differential Systems
by - Tata Institute of Fundamental Research ,
Contents: Parametrization of sets of integral submanifolds (Regular linear maps, Germs of submanifolds of a manifold); Exterior differential systems (Differential systems with independent variables); Prolongation of Exterior Differential Systems.
(8207 views) Discrete Differential Geometry: An Applied Introduction
by - Columbia University ,
This new and elegant area of mathematics has exciting applications, as this text demonstrates by presenting practical examples in geometry processing (surface fairing, parameterization, and remeshing) and simulation (of cloth, shells, rods, fluids).
(10940 views) Global Theory Of Minimal Surfaces
by - American Mathematical Society ,
The wide variety of topics covered make this volume suitable for graduate students and researchers interested in differential geometry. The subjects covered include minimal and constant-mean-curvature submanifolds, Lagrangian geometry, and more.
(7699 views) Ricci Flow and the Poincare Conjecture
by - American Mathematical Society ,
This book provides full details of a complete proof of the Poincare Conjecture following Grigory Perelman's preprints. The book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology.
(9038 views) Lectures on Calabi-Yau and Special Lagrangian Geometry
by - arXiv ,
An introduction to Calabi-Yau manifolds and special Lagrangian submanifolds from the differential geometric point of view, followed by recent results on singularities of special Lagrangian submanifolds, and their application to the SYZ Conjecture.
(9119 views) Notes on the Atiyah-Singer Index Theorem
by - University of Notre Dame ,
This is arguably one of the deepest and most beautiful results in modern geometry, and it is surely a must know for any geometer / topologist. It has to do with elliptic partial differential operators on a compact manifold.
(6724 views) An introductory course in differential geometry and the Atiyah-Singer index theorem
by - Binghamton University ,
This is a lecture-based class on the Atiyah-Singer index theorem, proved in the 60's by Sir Michael Atiyah and Isadore Singer. Their work on this theorem lead to a joint Abel prize in 2004. Requirements: Knowledge of topology and manifolds.
(7986 views) An Introduction to Gaussian Geometry
by - Lund University ,
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.
(8193 views) Introduction to Homological Geometry
by - arXiv ,
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.
(6314 views) Functional Differential Geometry
by - MIT ,
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.
(8170 views) Combinatorial Geometry with Application to Field Theory
by - InfoQuest ,
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.
(11088 views) Comparison Geometry
by - Cambridge University Press ,
This volume is an up-to-date panorama of Comparison Geometry, featuring surveys and new research. Surveys present classical and recent results, and often include complete proofs, in some cases involving a new and unified approach.
(7987 views) Tight and Taut Submanifolds
by - Cambridge University Press ,
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.
(7883 views) A Geometric Approach to Differential Forms
by - arXiv ,
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.
(10735 views) Probability, Geometry and Integrable Systems
by - Cambridge University Press ,
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.
(11429 views) Projective and Polar Spaces
by - Queen Mary College ,
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.
(8566 views) Exterior Differential Systems and Euler-Lagrange Partial Differential Equations
by - University Of Chicago Press ,
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.
(13172 views) Algebraic geometry and projective differential geometry
by - arXiv ,
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.
(11861 views) The Convenient Setting of Global Analysis
by - American Mathematical Society ,
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.
(10194 views) Cusps of Gauss Mappings
by - Pitman Advanced Pub. Program ,
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.
(11745 views) Natural Operations in Differential Geometry
by - Springer ,
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.
(12450 views) Projective Differential Geometry Old and New
by - Cambridge University Press ,
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.
(13498 views) Synthetic Differential Geometry
by - Cambridge University Press ,
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.
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