Download or read book Differential and Complex Geometry Origins Abstractions and Embeddings written by Raymond O. Wells, Jr. and published by Springer. This book was released on 2017-08-01 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential and complex geometry are two central areas of mathematics with a long and intertwined history. This book, the first to provide a unified historical perspective of both subjects, explores their origins and developments from the sixteenth to the twentieth century. Providing a detailed examination of the seminal contributions to differential and complex geometry up to the twentieth-century embedding theorems, this monograph includes valuable excerpts from the original documents, including works of Descartes, Fermat, Newton, Euler, Huygens, Gauss, Riemann, Abel, and Nash. Suitable for beginning graduate students interested in differential, algebraic or complex geometry, this book will also appeal to more experienced readers.
Download or read book Transcendence and Linear Relations of 1 Periods written by Annette Huber and published by Cambridge University Press. This book was released on 2022-05-26 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leading experts explore the relation between periods and transcendental numbers, using a modern approach derived from the theory of motives.
Download or read book Aspects of Differential Geometry V written by Esteban Calviño-Louzao and published by Morgan & Claypool Publishers. This book was released on 2021-04-06 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Book V completes the discussion of the first four books by treating in some detail the analytic results in elliptic operator theory used previously. Chapters 16 and 17 provide a treatment of the techniques in Hilbert space, the Fourier transform, and elliptic operator theory necessary to establish the spectral decomposition theorem of a self-adjoint operator of Laplace type and to prove the Hodge Decomposition Theorem that was stated without proof in Book II. In Chapter 18, we treat the de Rham complex and the Dolbeault complex, and discuss spinors. In Chapter 19, we discuss complex geometry and establish the Kodaira Embedding Theorem.
Download or read book Complex Differential Geometry written by Fangyang Zheng and published by American Mathematical Soc.. This book was released on 2000 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses the differential geometric aspects of complex manifolds. This work contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. It discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles. It also gives a brief account of the surface classification theory.
Download or read book Explorations in Complex and Riemannian Geometry written by John Bland and published by American Mathematical Soc.. This book was released on 2003 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 modern research. The material is intended for researchers and graduate students interested in several complex variables and complex geometry.
Download or read book Advances in Discrete Differential Geometry written by Alexander I. Bobenko and published by Springer. This book was released on 2016-08-12 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, and on pure mathematics and its practical applications. The interaction of these facets is demonstrated by concrete examples, including discrete conformal mappings, discrete complex analysis, discrete curvatures and special surfaces, discrete integrable systems, conformal texture mappings in computer graphics, and free-form architecture. This richly illustrated book will convince readers that this new branch of mathematics is both beautiful and useful. It will appeal to graduate students and researchers in differential geometry, complex analysis, mathematical physics, numerical methods, discrete geometry, as well as computer graphics and geometry processing.
Download or read book Advances in Complex Geometry written by Yanir A. Rubinstein and published by American Mathematical Soc.. This book was released on 2019-08-26 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains contributions from speakers at the 2015–2018 joint Johns Hopkins University and University of Maryland Complex Geometry Seminar. It begins with a survey article on recent developments in pluripotential theory and its applications to Kähler–Einstein metrics and continues with articles devoted to various aspects of the theory of complex manifolds and functions on such manifolds.
Download or read book Complex Geometry written by Daniel Huybrechts and published by . This book was released on 2005 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discrete Differential Geometry written by Alexander I. Bobenko TU Berlin and published by Springer Science & Business Media. This book was released on 2008-03-27 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book on a newly emerging field of discrete differential geometry providing an excellent way to access this exciting area. It provides discrete equivalents of the geometric notions and methods of differential geometry, such as notions of curvature and integrability for polyhedral surfaces. The carefully edited collection of essays gives a lively, multi-facetted introduction to this emerging field.
Download or read book Topics in Mathematical Analysis and Differential Geometry written by Nicolas K. Laos and published by World Scientific. This book was released on 1998 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the interplay between mathematical analysis and differential geometry as well as the foundations of these two fields. The development of a unified approach to topological vector spaces, differential geometry and algebraic and differential topology of function manifolds led to the broad expansion of global analysis. This book serves as a self-contained reference on both the prerequisites for further study and the recent research results which have played a decisive role in the advancement of global analysis.
Download or read book Vector Bundles and Complex Geometry written by Oscar García-Prada and published by American Mathematical Soc.. This book was released on 2010-01-01 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of papers from the conference on Vector Bundles held at Miraflores de la sierra, Madrid, Spain on June 16-20, 2008, which honored S. Ramanan on his 70th birthday. The main areas covered in this volume are vector bundles, parabolic bundles, abelian varieties, hilbert schemes, contact structures, index theory, Hodge theory, and geometric invariant theory. Professor Ramanan has made important contributions in all of these areas.
Download or read book A First Course in Geometric Topology and Differential Geometry written by Ethan D. Bloch and published by Springer Science & Business Media. This book was released on 1997 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: The uniqueness of this text in combining geometric topology and differential geometry lies in its unifying thread: the notion of a surface. With numerous illustrations, exercises and examples, the student comes to understand the relationship of the modern abstract approach to geometric intuition. The text is kept at a concrete level, avoiding unnecessary abstractions, yet never sacrificing mathematical rigor. The book includes topics not usually found in a single book at this level.
Download or read book Complex Manifolds and Hyperbolic Geometry written by Clifford J. Earle and published by American Mathematical Soc.. This book was released on 2002 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume derives from the second Iberoamerican Congress on Geometry, held in 2001 in Mexico at the Centro de Investigacion en Matematicas A.C., an internationally recognized program of research in pure mathematics. The conference topics were chosen with an eye toward the presentation of new methods, recent results, and the creation of more interconnections between the different research groups working in complex manifolds and hyperbolic geometry. This volume reflects both the unity and the diversity of these subjects. Researchers around the globe have been working on problems concerning Riemann surfaces, as well as a wide scope of other issues: the theory of Teichmuller spaces, theta functions, algebraic geometry and classical function theory. Included here are discussions revolving around questions of geometry that are related in one way or another to functions of a complex variable. There are contributors on Riemann surfaces, hyperbolic geometry, Teichmuller spaces, and quasiconformal maps. Complex geometry has many applications--triangulations of surfaces, combinatorics, ordinary differential equations, complex dynamics, and the geometry of special curves and jacobians, among others. In this book, research mathematicians in complex geometry, hyperbolic geometry and Teichmuller spaces will find a selection of strong papers by international experts.
Download or read book Differential Geometry written by Loring W. Tu and published by Springer. This book was released on 2017-06-15 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of de Rham cohomology is required for the last third of the text. Prerequisite material is contained in author's text An Introduction to Manifolds, and can be learned in one semester. For the benefit of the reader and to establish common notations, Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions such as the tensor product and the exterior power are included. Differential geometry, as its name implies, is the study of geometry using differential calculus. It dates back to Newton and Leibniz in the seventeenth century, but it was not until the nineteenth century, with the work of Gauss on surfaces and Riemann on the curvature tensor, that differential geometry flourished and its modern foundation was laid. Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory. Differential geometry is also useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among other fields. The field has even found applications to group theory as in Gromov's work and to probability theory as in Diaconis's work. It is not too far-fetched to argue that differential geometry should be in every mathematician's arsenal.
Download or read book Aspects of Differential Geometry IV written by Esteban Calviño-Louzao and published by Morgan & Claypool. This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Book IV continues the discussion begun in the first three volumes. Although it is aimed at first-year graduate students, it is also intended to serve as a basic reference for people working in affine differential geometry. It also should be accessible to undergraduates interested in affine differential geometry. We are primarily concerned with the study of affine surfaces which are locally homogeneous. We discuss affine gradient Ricci solitons, affine Killing vector fields, and geodesic completeness. Opozda has classified the affine surface geometries which are locally homogeneous; we follow her classification. Up to isomorphism, there are two simply connected Lie groups of dimension 2. The translation group ℝ2 is Abelian and the + group is non-Abelian. The first chapter presents foundational material. The second chapter deals with Type surfaces. These are the left-invariant affine geometries on ℝ2. Associating to each Type surface the space of solutions to the quasi-Einstein equation corresponding to the eigenvalue = -1 turns out to be a very powerful technique and plays a central role in our study as it links an analytic invariant with the underlying geometry of the surface. The third chapter deals with Type surfaces; these are the left-invariant affine geometries on the + group. These geometries form a very rich family which is only partially understood. The only remaining homogeneous geometry is that of the sphere 2. The fourth chapter presents relations between the geometry of an affine surface and the geometry of the cotangent bundle equipped with the neutral signature metric of the modified Riemannian extension.
Download or read book Complex and Differential Geometry written by Wolfgang Ebeling and published by Springer. This book was released on 2013-08-03 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the Proceedings of the conference "Complex and Differential Geometry 2009", held at Leibniz Universität Hannover, September 14 - 18, 2009. It was the aim of this conference to bring specialists from differential geometry and (complex) algebraic geometry together and to discuss new developments in and the interaction between these fields. Correspondingly, the articles in this book cover a wide area of topics, ranging from topics in (classical) algebraic geometry through complex geometry, including (holomorphic) symplectic and poisson geometry, to differential geometry (with an emphasis on curvature flows) and topology.
Download or read book Differential Geometry written by Heinrich Walter Guggenheimer and published by Courier Dover Publications. This book was released on 1963 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt:
