Differential And Complex Geometry Origins Abstractions And Embeddings
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Differential And Complex Geometry Origins Abstractions And Embeddings
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Author : Raymond O. Wells, Jr.
language : en
Publisher: Springer
Release Date : 2017-08-01
Differential And Complex Geometry Origins Abstractions And Embeddings written by Raymond O. Wells, Jr. and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-01 with Mathematics categories.
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.
Transcendence And Linear Relations Of 1 Periods
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Author : Annette Huber
language : en
Publisher: Cambridge University Press
Release Date : 2022-05-26
Transcendence And Linear Relations Of 1 Periods written by Annette Huber and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-26 with Mathematics categories.
Leading experts explore the relation between periods and transcendental numbers, using a modern approach derived from the theory of motives.
Aspects Of Differential Geometry V
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Author : Esteban Calviño-Louzao
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2021-04-06
Aspects Of Differential Geometry V written by Esteban Calviño-Louzao and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-06 with Mathematics categories.
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.
Complex Differential Geometry
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Author : Fangyang Zheng
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Complex Differential Geometry written by Fangyang Zheng and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Complex manifolds categories.
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.
Differential Geometry
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Author : Loring W. Tu
language : en
Publisher: Springer
Release Date : 2018-08-01
Differential Geometry written by Loring W. Tu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-01 with Mathematics categories.
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.
Introduction To Differential Geometry
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Author : Joel W. Robbin
language : en
Publisher: Springer Nature
Release Date : 2022-01-12
Introduction To Differential Geometry written by Joel W. Robbin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-12 with Mathematics categories.
This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point. The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor. An additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.
Explorations In Complex And Riemannian Geometry
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Author : Robert Everist Greene
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Explorations In Complex And Riemannian Geometry written by Robert Everist Greene and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
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.
Differential Geometry And Topology
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Author : Jacob T. Schwartz
language : en
Publisher: M.E. Sharpe
Release Date : 1968
Differential Geometry And Topology written by Jacob T. Schwartz and has been published by M.E. Sharpe this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Mathematics categories.
Complex Geometry
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Author : Daniel Huybrechts
language : en
Publisher:
Release Date : 2005
Complex Geometry written by Daniel Huybrechts and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Geometry, Algebraic categories.
Complex Manifolds And Hyperbolic Geometry
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Author : Clifford J. Earle
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Complex Manifolds And Hyperbolic Geometry written by Clifford J. Earle and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
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.