Topological Differential And Conformal Geometry Of Surfaces
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Topological Differential And Conformal Geometry Of Surfaces
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Author : Norbert A'Campo
language : en
Publisher: Springer Nature
Release Date : 2021-10-27
Topological Differential And Conformal Geometry Of Surfaces written by Norbert A'Campo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-27 with Mathematics categories.
This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces. It first covers the prerequisites, including the basics of differential forms, the Poincaré Lemma, the Morse Lemma, the classification of compact connected oriented surfaces, Stokes’ Theorem, fixed point theorems and rigidity theorems. There is also a novel presentation of planar hyperbolic geometry. Moving on to more advanced concepts, it covers topics such as Riemannian metrics, the isometric torsion-free connection on vector fields, the Ansatz of Koszul, the Gauss–Bonnet Theorem, and integrability. These concepts are then used for the study of Riemann surfaces. One of the focal points is the Uniformization Theorem for compact surfaces, an elementary proof of which is given via a property of the energy functional. Among numerous other results, there is also a proof of Chow’s Theorem on compact holomorphic submanifolds in complex projective spaces. Based on lecture courses given by the author, the book will be accessible to undergraduates and graduates interested in the analytic theory of Riemann surfaces.
Topological Differential And Conformal Geometry Of Surfaces
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Author : Norbert A'Campo
language : en
Publisher: Springer
Release Date : 2021-10-28
Topological Differential And Conformal Geometry Of Surfaces written by Norbert A'Campo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-28 with Mathematics categories.
This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces. It first covers the prerequisites, including the basics of differential forms, the Poincaré Lemma, the Morse Lemma, the classification of compact connected oriented surfaces, Stokes’ Theorem, fixed point theorems and rigidity theorems. There is also a novel presentation of planar hyperbolic geometry. Moving on to more advanced concepts, it covers topics such as Riemannian metrics, the isometric torsion-free connection on vector fields, the Ansatz of Koszul, the Gauss–Bonnet Theorem, and integrability. These concepts are then used for the study of Riemann surfaces. One of the focal points is the Uniformization Theorem for compact surfaces, an elementary proof of which is given via a property of the energy functional. Among numerous other results, there is also a proof of Chow’s Theorem on compact holomorphic submanifolds in complex projective spaces. Based on lecture courses given by the author, the book will be accessible to undergraduates and graduates interested in the analytic theory of Riemann surfaces.
Topological Differential And Conformal Geometry Of Surfaces
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Author : Norbert A'Campo
language : en
Publisher:
Release Date : 2021
Topological Differential And Conformal Geometry Of Surfaces written by Norbert A'Campo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces. It first covers the prerequisites, including the basics of differential forms, the Poincaré Lemma, the Morse Lemma, the classification of compact connected oriented surfaces, Stokes' Theorem, fixed point theorems and rigidity theorems. There is also a novel presentation of planar hyperbolic geometry. Moving on to more advanced concepts, it covers topics such as Riemannian metrics, the isometric torsion-free connection on vector fields, the Ansatz of Koszul, the Gauss-Bonnet Theorem, and integrability. These concepts are then used for the study of Riemann surfaces. One of the focal points is the Uniformization Theorem for compact surfaces, an elementary proof of which is given via a property of the energy functional. Among numerous other results, there is also a proof of Chow's Theorem on compact holomorphic submanifolds in complex projective spaces. Based on lecture courses given by the author, the book will be accessible to undergraduates and graduates interested in the analytic theory of Riemann surfaces.
Computational Conformal Geometry
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Author : Xianfeng David Gu
language : en
Publisher:
Release Date : 2008
Computational Conformal Geometry written by Xianfeng David Gu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with CD-ROMs categories.
"Computational conformal geometry is an emerging inter-disciplinary field, which applies algebraic topology, differential geometry and Riemann surface theories in geometric modelling, computer graphics, computer vision, medical imaging, visualization, scientifice computations and many other engineering fields."--Back cover.
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.
Elementary Differential Geometry
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Author : Barrett O'Neill
language : en
Publisher: Academic Press
Release Date : 2014-05-12
Elementary Differential Geometry written by Barrett O'Neill and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
Elementary Differential Geometry focuses on the elementary account of the geometry of curves and surfaces. The book first offers information on calculus on Euclidean space and frame fields. Topics include structural equations, connection forms, frame fields, covariant derivatives, Frenet formulas, curves, mappings, tangent vectors, and differential forms. The publication then examines Euclidean geometry and calculus on a surface. Discussions focus on topological properties of surfaces, differential forms on a surface, integration of forms, differentiable functions and tangent vectors, congruence of curves, derivative map of an isometry, and Euclidean geometry. The manuscript takes a look at shape operators, geometry of surfaces in E, and Riemannian geometry. Concerns include geometric surfaces, covariant derivative, curvature and conjugate points, Gauss-Bonnet theorem, fundamental equations, global theorems, isometries and local isometries, orthogonal coordinates, and integration and orientation. The text is a valuable reference for students interested in elementary differential geometry.
Mostly Surfaces
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Author : Richard Evan Schwartz
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Mostly Surfaces written by Richard Evan Schwartz 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 2011 with Mathematics categories.
The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.
Geometry And Topology Of Submanifolds Iv Proceedings Of The Conference On Differential Geometry And Vision
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Author : Franki Dillen
language : en
Publisher: World Scientific
Release Date : 1992-07-17
Geometry And Topology Of Submanifolds Iv Proceedings Of The Conference On Differential Geometry And Vision written by Franki Dillen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-07-17 with categories.
This proceedings on pure and applied differential geometry, discusses several subjects in submanifold theory, such as the Willmore problem, minimal surfaces, submanifolds of finite type, affine differential geometry, indefinite Riemannian geometry, and applications of differential geometry in human and artificial vision.
Lectures On Classical Differential Geometry
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Author : Dirk Jan Struik
language : en
Publisher: Courier Corporation
Release Date : 1961-01-01
Lectures On Classical Differential Geometry written by Dirk Jan Struik and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961-01-01 with Mathematics categories.
Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student. Written by a noted mathematician and historian of mathematics, this volume presents the fundamental conceptions of the theory of curves and surfaces and applies them to a number of examples. Dr. Struik has enhanced the treatment with copious historical, biographical, and bibliographical references that place the theory in context and encourage the student to consult original sources and discover additional important ideas there. For this second edition, Professor Struik made some corrections and added an appendix with a sketch of the application of Cartan's method of Pfaffians to curve and surface theory. The result was to further increase the merit of this stimulating, thought-provoking text — ideal for classroom use, but also perfectly suited for self-study. In this attractive, inexpensive paperback edition, it belongs in the library of any mathematician or student of mathematics interested in differential geometry.
Surveys In Geometry Ii
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Author : Athanase Papadopoulos
language : en
Publisher: Springer Nature
Release Date : 2024-05-27
Surveys In Geometry Ii written by Athanase Papadopoulos and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-27 with Mathematics categories.
The book is the second volume of a collection which consists of surveys that focus on important topics in geometry which are at the heart of current research. The topics in the present volume include the conformal and the metric geometry of surfaces, Teichmüller spaces, immersed surfaces of prescribed extrinsic curvature in 3-dimensional manifolds, symplectic geometry, the metric theory of Grassmann spaces, homogeneous metric spaces, polytopes, the higher-dimensional Gauss–Bonnet formula, isoperimetry in finitely generated groups and Coxeter groups. Each chapter is intended for graduate students and researchers. Several chapters are based on lectures given by their authors to middle-advanced level students and young researchers. The whole book is intended to be an introduction to important topics in geometry.