Introduction To Complex Hyperbolic Spaces
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Introduction To Complex Hyperbolic Spaces
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Author : Serge Lang
language : en
Publisher: Springer
Release Date : 2014-01-15
Introduction To Complex Hyperbolic Spaces written by Serge Lang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Introduction To Complex Hyperbolic Spaces
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Introduction To Complex Hyperbolic Spaces written by Serge Lang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Since the appearance of Kobayashi's book, there have been several re sults at the basic level of hyperbolic spaces, for instance Brody's theorem, and results of Green, Kiernan, Kobayashi, Noguchi, etc. which make it worthwhile to have a systematic exposition. Although of necessity I re produce some theorems from Kobayashi, I take a different direction, with different applications in mind, so the present book does not super sede Kobayashi's. My interest in these matters stems from their relations with diophan tine geometry. Indeed, if X is a projective variety over the complex numbers, then I conjecture that X is hyperbolic if and only if X has only a finite number of rational points in every finitely generated field over the rational numbers. There are also a number of subsidiary conjectures related to this one. These conjectures are qualitative. Vojta has made quantitative conjectures by relating the Second Main Theorem of Nevan linna theory to the theory of heights, and he has conjectured bounds on heights stemming from inequalities having to do with diophantine approximations and implying both classical and modern conjectures. Noguchi has looked at the function field case and made substantial progress, after the line started by Grauert and Grauert-Reckziegel and continued by a recent paper of Riebesehl. The book is divided into three main parts: the basic complex analytic theory, differential geometric aspects, and Nevanlinna theory. Several chapters of this book are logically independent of each other.
Introduction To Complex Hyperbolic Spaces
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 1987-05-04
Introduction To Complex Hyperbolic Spaces written by Serge Lang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-05-04 with Mathematics categories.
Since the appearance of Kobayashi's book, there have been several re sults at the basic level of hyperbolic spaces, for instance Brody's theorem, and results of Green, Kiernan, Kobayashi, Noguchi, etc. which make it worthwhile to have a systematic exposition. Although of necessity I re produce some theorems from Kobayashi, I take a different direction, with different applications in mind, so the present book does not super sede Kobayashi's. My interest in these matters stems from their relations with diophan tine geometry. Indeed, if X is a projective variety over the complex numbers, then I conjecture that X is hyperbolic if and only if X has only a finite number of rational points in every finitely generated field over the rational numbers. There are also a number of subsidiary conjectures related to this one. These conjectures are qualitative. Vojta has made quantitative conjectures by relating the Second Main Theorem of Nevan linna theory to the theory of heights, and he has conjectured bounds on heights stemming from inequalities having to do with diophantine approximations and implying both classical and modern conjectures. Noguchi has looked at the function field case and made substantial progress, after the line started by Grauert and Grauert-Reckziegel and continued by a recent paper of Riebesehl. The book is divided into three main parts: the basic complex analytic theory, differential geometric aspects, and Nevanlinna theory. Several chapters of this book are logically independent of each other.
Complex Hyperbolic Geometry
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Author : William Mark Goldman
language : en
Publisher: Oxford University Press
Release Date : 1999
Complex Hyperbolic Geometry written by William Mark Goldman and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Complex hyperbolic geometry is a particularly rich area of study, enhanced by the confluence of several areas of research including Riemannian geometry, complex analysis, symplectic and contact geometry, Lie group theory, and harmonic analysis. The boundary of complex hyperbolic geometry, known as spherical CR or Heisenberg geometry, is equally rich, and although there exist accounts of analysis in such spaces there is currently no account of their geometry. This book redresses the balance and provides an overview of the geometry of both the complex hyperbolic space and its boundary. Motivated by applications of the theory to geometric structures, moduli spaces and discrete groups, it is designed to provide an introduction to this fascinating and important area and invite further research and development.
Hyperbolic Geometry
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Author : James W. Anderson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Hyperbolic Geometry written by James W. Anderson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This book provides a self-contained introduction to the subject, providing the reader with a firm grasp of the concepts and techniques of this beautiful area of mathematics. Topics covered include the upper half-space model of the hyperbolic plane, Möbius transformations, the general Möbius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincaré disc model, convex subsets of the hyperbolic plane, and the Gauss-Bonnet formula for the area of a hyperbolic polygon and its applications. This updated second edition also features: - an expanded discussion of planar models of the hyperbolic plane arising from complex analysis; - the hyperboloid model of the hyperbolic plane; - a brief discussion of generalizations to higher dimensions; - many new exercises.
Complex Kleinian Groups
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Author : Angel Cano
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-05
Complex Kleinian Groups written by Angel Cano and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-05 with Mathematics categories.
This monograph lays down the foundations of the theory of complex Kleinian groups, a newly born area of mathematics whose origin traces back to the work of Riemann, Poincaré, Picard and many others. Kleinian groups are, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can be regarded too as being groups of holomorphic automorphisms of the complex projective line CP1. When going into higher dimensions, there is a dichotomy: Should we look at conformal automorphisms of the n-sphere?, or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories are different in higher dimensions. In the first case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition. In the second case we are talking about an area of mathematics that still is in its childhood, and this is the focus of study in this monograph. This brings together several important areas of mathematics, as for instance classical Kleinian group actions, complex hyperbolic geometry, chrystallographic groups and the uniformization problem for complex manifolds.
Foundations Of Hyperbolic Manifolds
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Author : John Ratcliffe
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Foundations Of Hyperbolic Manifolds written by John Ratcliffe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. Particular emphasis has been placed on readability and completeness of ar gument. The treatment of the material is for the most part elementary and self-contained. The reader is assumed to have a basic knowledge of algebra and topology at the first-year graduate level of an American university. The book is divided into three parts. The first part, consisting of Chap ters 1-7, is concerned with hyperbolic geometry and basic properties of discrete groups of isometries of hyperbolic space. The main results are the existence theorem for discrete reflection groups, the Bieberbach theorems, and Selberg's lemma. The second part, consisting of Chapters 8-12, is de voted to the theory of hyperbolic manifolds. The main results are Mostow's rigidity theorem and the determination of the structure of geometrically finite hyperbolic manifolds. The third part, consisting of Chapter 13, in tegrates the first two parts in a development of the theory of hyperbolic orbifolds. The main results are the construction of the universal orbifold covering space and Poincare's fundamental polyhedron theorem.
Real Hypersurfaces In Hermitian Symmetric Spaces
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Author : Jürgen Berndt
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-03-21
Real Hypersurfaces In Hermitian Symmetric Spaces written by Jürgen Berndt and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-21 with Mathematics categories.
Hermitian symmetric spaces are an important class of manifolds that can be studied with methods from Kähler geometry and Lie theory. This work gives an introduction to Hermitian symmetric spaces and their submanifolds, and presents classifi cation results for real hypersurfaces in these spaces, focusing on results obtained by Jürgen Berndt and Young Jin Suh in the last 20 years.
Geometry And Analysis On Manifolds
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Author : Takushiro Ochiai
language : en
Publisher: Springer
Release Date : 2015-02-25
Geometry And Analysis On Manifolds written by Takushiro Ochiai and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-25 with Mathematics categories.
This volume is dedicated to the memory of Shoshichi Kobayashi, and gathers contributions from distinguished researchers working on topics close to his research areas. The book is organized into three parts, with the first part presenting an overview of Professor Shoshichi Kobayashi’s career. This is followed by two expository course lectures (the second part) on recent topics in extremal Kähler metrics and value distribution theory, which will be helpful for graduate students in mathematics interested in new topics in complex geometry and complex analysis. Lastly, the third part of the volume collects authoritative research papers on differential geometry and complex analysis. Professor Shoshichi Kobayashi was a recognized international leader in the areas of differential and complex geometry. He contributed crucial ideas that are still considered fundamental in these fields. The book will be of interest to researchers in the fields of differential geometry, complex geometry, and several complex variables geometry, as well as to graduate students in mathematics.
Prospects Of Differential Geometry And Its Related Fields Proceedings Of The 3rd International Colloquium On Differential Geometry And Its Related Fields
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Author : Toshiaki Adachi
language : en
Publisher: World Scientific
Release Date : 2013-09-24
Prospects Of Differential Geometry And Its Related Fields Proceedings Of The 3rd International Colloquium On Differential Geometry And Its Related Fields written by Toshiaki Adachi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-24 with Mathematics categories.
This volume consists of contributions by the main participants of the 3rd International Colloquium on Differential Geometry and its Related Fields (ICDG2012), which was held in Veliko Tarnovo, Bulgaria. Readers will find original papers by specialists and well-organized reports of recent developments in the fields of differential geometry, complex analysis, information geometry, mathematical physics and coding theory. This volume provides significant information that will be useful to researchers and serves as a good guide for young scientists. It is also for those who wish to start investigating these topics and interested in their interdisciplinary areas.