# Introduction to Complex Hyperbolic Spaces 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.

Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 9781475719451

Category: Mathematics

Page: 272

View: 215

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.
2013-03-09

# Hyperbolic Complex Spaces (I prefer to put the adjective hyperbolic before “complex space” since a “complex hyperbolic space” would often mean a complex space form, i.e., ... I introduced the intrinsic pseudo-distance dx in ...

Author: Shoshichi Kobayashi

Publisher: Springer Science & Business Media

ISBN: 9783662035825

Category: Mathematics

Page: 474

View: 688

In the three decades since the introduction of the Kobayashi distance, the subject of hyperbolic complex spaces and holomorphic mappings has grown to be a big industry. This book gives a comprehensive and systematic account on the Carathéodory and Kobayashi distances, hyperbolic complex spaces and holomorphic mappings with geometric methods. A very complete list of references should be useful for prospective researchers in this area.
2013-03-09

# Hyperbolic Manifolds and Holomorphic Mappings I introduced the intrinsic pseudodistance dX in 1967 and published the first edition of this monograph in 1970 and a survey ... In the 35 years since the appearance of the first edition, the subject of hyperbolic complex spaces has seen ...

Author: Shoshichi Kobayashi

Publisher: World Scientific Publishing Company

ISBN: 9789813101937

Category: Mathematics

Page: 160

View: 928

The first edition of this influential book, published in 1970, opened up a completely new field of invariant metrics and hyperbolic manifolds. The large number of papers on the topics covered by the book written since its appearance led Mathematical Reviews to create two new subsections “invariant metrics and pseudo-distances” and “hyperbolic complex manifolds” within the section “holomorphic mappings”. The invariant distance introduced in the first edition is now called the “Kobayashi distance”, and the hyperbolicity in the sense of this book is called the “Kobayashi hyperbolicity” to distinguish it from other hyperbolicities. This book continues to serve as the best introduction to hyperbolic complex analysis and geometry and is easily accessible to students since very little is assumed. The new edition adds comments on the most recent developments in the field.
2005-11-02

# Geometry of Riemann Surfaces Later, work of Chen and Greenberg and of Mostow on symmetric spaces led to a resurgence of interest in complex hyperbolic discrete groups. The basic theory of complex hyperbolic quasi-Fuchsian groups was laid out by Goldman and these ...

Author: Frederick P. Gardiner

Publisher: Cambridge University Press

ISBN: 9780521733076

Category: Mathematics

Page: 395

View: 608

Riemann surfaces is a thriving area of mathematics with applications to hyperbolic geometry, complex analysis, conformal dynamics, discrete groups, algebraic curves and more. This collection of articles presents original research and expert surveys of important related topics, making the field accessible to research workers, graduate students and teachers.
2010-02-11

# Real Hypersurfaces in Hermitian Symmetric Spaces Real hypersurfaces in complex projective spaces and in complex hyperbolic spaces have been of interest to geometers since many years. A thorough introduction and overview to this topic can be found in the excellent monograph [→33] by ...

Author: Jürgen Berndt

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 9783110689914

Category: Mathematics

Page: 388

View: 275

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 classification results for real hypersurfaces in these spaces, focusing on results obtained by Jürgen Berndt and Young Jin Suh in the last 20 years.
2022-04-04

# Trends in Complex Analysis Differential Geometry and Mathematical Physics KAHLER MAGNETIC, FIELDS ON A PRODUCT OF COMPLEX HYPERBOLIC SPACES TOSHIAKI ADACHI Department of Mathematics Nagoya ... spaces from the viewpoints of cyclicity semi conjugacy of magnetic flows and asymptotic behavior 1 Introduction Let ...

Author: Stancho Dimiev

Publisher: World Scientific

ISBN: 9789812704191

Category: Electronic books

Page: 237

View: 682

The Sixth International Workshop on Complex Structures and Vector Fields was a continuation of the previous five workshops (1992, 1994, 1996, 1998, 2000) on similar research projects. This series of workshops aims at higher achievements in studies of new research subjects. The present volume will meet with the satisfaction of many readers.
2003

# Trends in Complex Analysis Differential Geometry and Mathematical Physics KAHLER MAGNETIC, FIELDS ON A PRODUCT OF COMPLEX HYPERBOLIC SPACES TOSHIAKI ADACHI Department of Mathematics Nagoya ... spaces from the viewpoints of cyclicity semi conjugacy of magnetic flows and asymptotic behavior 1 Introduction Let ...

Author: Stancho Dimiev

Publisher: World Scientific

ISBN: 9789814485456

Category: Mathematics

Page: 248

View: 994

' The Sixth International Workshop on Complex Structures and Vector Fields was a continuation of the previous five workshops (1992, 1994, 1996, 1998, 2000) on similar research projects. This series of workshops aims at higher achievements in studies of new research subjects. The present volume will meet with the satisfaction of many readers. Contents:Real Analytic Almost Complex Manifolds (L N Apostolova)Involutive Distributions of Codimension One in Kaehler Manifolds (G Ganchev)Three Theorems on Isotropic Immersions (S Maeda)On the Meilikhson Theorem (M S Marinov)Curvature Tensors on Almost Contact Manifolds with B-Metric (G Nakova)Complex Structures and the Quark Confinement (I B Pestov)Curvature Operators in the Relativity (V Videv & Y Tsankov)On Integrability of Almost Quaternionic Manifolds (A Yamada)and other papers Readership: Graduate students and researchers in complex analysis, differential geometry and mathematical physics. Keywords:Poincare Formulae;Oka''s Theorem;Quantum Field Theory;Time-Like Killing Vector Field;Kaehler Immersion;Circle;Integrability of Almost Hermitian Manifold;Hyperocmplex Manifold;Semi-Symmetric Space;Hypercomplex Manifold'
2003-06-13

# Geometry and Analysis on Manifolds [KO75] S. Kobayashi and T. Ochiai, Meromorphic mappings onto compact complex spaces of general type, Invent. Math. 31 (1975), 7–16. [La60] S. Lang, Integral points on curves, ... [La87] ——, Introduction to Complex Hyperbolic Spaces, ...

Author: Takushiro Ochiai

Publisher: Springer

ISBN: 9783319115238

Category: Mathematics

Page: 481

View: 787

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.
2015-02-25

# Invariant Distances and Metrics in Complex Analysis S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Pure and Applied Mathematics 2, M. Dekker, 1970. S. Kobayashi, Some remarks and ... S. Lang, Introduction to Complex Hyperbolic Spaces, Springer Verlag, 1987. 830 Bibliography.

Author: Marek Jarnicki

Publisher: Walter de Gruyter

ISBN: 9783110253863

Category: Mathematics

Page: 878

View: 374

As in the field of "Invariant Distances and Metrics in Complex Analysis" there was and is a continuous progress this is now the second extended edition of the corresponding monograph. This comprehensive book is about the study of invariant pseudodistances (non-negative functions on pairs of points) and pseudometrics (non-negative functions on the tangent bundle) in several complex variables. It is an overview over a highly active research area at the borderline between complex analysis, functional analysis and differential geometry. New chapters are covering the Wu, Bergman and several other metrics. The book considers only domains in Cn and assumes a basic knowledge of several complex variables. It is a valuable reference work for the expert but is also accessible to readers who are knowledgeable about several complex variables. Each chapter starts with a brief summary of its contents and continues with a short introduction. It ends with an "Exercises" and a "List of problems" section that gathers all the problems from the chapter. The authors have been highly successful in giving a rigorous but readable account of the main lines of development in this area.
2013-06-26

# Number Theory III Introduction to Complex Hyperbolic Spaces Since its introduction by Kobayashi , the theory of complex hyperbolic spaces has progressed considerably . This book gives an account of some of the most important results , such as Brody's ...

Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 3540612238

Category: Mathematics

Page: 296

View: 102