Selected Topics in Cauchy-Riemann Geometry
| Author | : Sorin Dragomir |
| Publisher | : |
| Total Pages | : 402 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : |
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Selected Topics In Cauchy Riemann Geometry PDF Download
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Hermitian Analysis
| Author | : John P. D'Angelo |
| Publisher | : Springer |
| Total Pages | : 229 |
| Release | : 2019-05-24 |
| Genre | : Mathematics |
| ISBN | : 3030165140 |
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This textbook provides a coherent, integrated look at various topics from undergraduate analysis. It begins with Fourier series, continues with Hilbert spaces, discusses the Fourier transform on the real line, and then turns to the heart of the book, geometric considerations. This chapter includes complex differential forms, geometric inequalities from one and several complex variables, and includes some of the author's original results. The concept of orthogonality weaves the material into a coherent whole. This textbook will be a useful resource for upper-undergraduate students who intend to continue with mathematics, graduate students interested in analysis, and researchers interested in some basic aspects of Cauchy-Riemann (CR) geometry. The inclusion of several hundred exercises makes this book suitable for a capstone undergraduate Honors class. This second edition contains a significant amount of new material, including a new chapter dedicated to the CR geometry of the unit sphere. This chapter builds upon the first edition by presenting recent results about groups associated with CR sphere maps. From reviews of the first edition: The present book developed from the teaching experiences of the author in several honors courses. .... All the topics are motivated very nicely, and there are many exercises, which make the book ideal for a first-year graduate course on the subject. .... The style is concise, always very neat, and proofs are given with full details. Hence, I certainly suggest this nice textbook to anyone interested in the subject, even for self-study. Fabio Nicola, Politecnico di Torino, Mathematical Reviews D’Angelo has written an eminently readable book, including excellent explanations of pretty nasty stuff for even the more gifted upper division players .... It certainly succeeds in hooking the present browser: I like this book a great deal. Michael Berg, Loyola Marymount University, Mathematical Association of America
Hermitian Analysis
| Author | : John P. D'Angelo |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 211 |
| Release | : 2013-09-24 |
| Genre | : Mathematics |
| ISBN | : 1461485266 |
Download Hermitian Analysis Book in PDF, ePub and Kindle
Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry provides a coherent, integrated look at various topics from undergraduate analysis. It begins with Fourier series, continues with Hilbert spaces, discusses the Fourier transform on the real line, and then turns to the heart of the book, geometric considerations. This chapter includes complex differential forms, geometric inequalities from one and several complex variables, and includes some of the author's results. The concept of orthogonality weaves the material into a coherent whole. This textbook will be a useful resource for upper-undergraduate students who intend to continue with mathematics, graduate students interested in analysis, and researchers interested in some basic aspects of CR Geometry. The inclusion of several hundred exercises makes this book suitable for a capstone undergraduate Honors class.
Foliations in Cauchy-Riemann Geometry
| Author | : Elisabetta Barletta |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 270 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821843044 |
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The authors study the relationship between foliation theory and differential geometry and analysis on Cauchy-Riemann (CR) manifolds. The main objects of study are transversally and tangentially CR foliations, Levi foliations of CR manifolds, solutions of the Yang-Mills equations, tangentially Monge-Ampere foliations, the transverse Beltrami equations, and CR orbifolds. The novelty of the authors' approach consists in the overall use of the methods of foliation theory and choice of specific applications. Examples of such applications are Rea's holomorphic extension of Levi foliations, Stanton's holomorphic degeneracy, Boas and Straube's approximately commuting vector fields method for the study of global regularity of Neumann operators and Bergman projections in multi-dimensional complex analysis in several complex variables, as well as various applications to differential geometry. Many open problems proposed in the monograph may attract the mathematical community and lead to further applications of
On the Hypotheses Which Lie at the Bases of Geometry
| Author | : Bernhard Riemann |
| Publisher | : Birkhäuser |
| Total Pages | : 181 |
| Release | : 2016-04-19 |
| Genre | : Mathematics |
| ISBN | : 3319260421 |
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This book presents William Clifford’s English translation of Bernhard Riemann’s classic text together with detailed mathematical, historical and philosophical commentary. The basic concepts and ideas, as well as their mathematical background, are provided, putting Riemann’s reasoning into the more general and systematic perspective achieved by later mathematicians and physicists (including Helmholtz, Ricci, Weyl, and Einstein) on the basis of his seminal ideas. Following a historical introduction that positions Riemann’s work in the context of his times, the history of the concept of space in philosophy, physics and mathematics is systematically presented. A subsequent chapter on the reception and influence of the text accompanies the reader from Riemann’s times to contemporary research. Not only mathematicians and historians of the mathematical sciences, but also readers from other disciplines or those with an interest in physics or philosophy will find this work both appealing and insightful.
Selected Topics in Algebraic Geometry
| Author | : National Research Council (U.S.). Committee on Rational Transformations |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 518 |
| Release | : 1970 |
| Genre | : Mathematics |
| ISBN | : 9780828401890 |
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This book resulted from two reports (published in 1928 and 1932) of the Committee on Rational Transformations, established by the National Research Council. The purpose of the reports was to give a comprehensive survey of the literature on the subject. Each chapter is regarded as a separate unit that can be read independently.
Geometric Control Theory and Sub-Riemannian Geometry
| Author | : Gianna Stefani |
| Publisher | : Springer |
| Total Pages | : 385 |
| Release | : 2014-06-05 |
| Genre | : Mathematics |
| ISBN | : 331902132X |
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Honoring Andrei Agrachev's 60th birthday, this volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume, etc.
Geometry of Cauchy-Riemann Submanifolds
| Author | : Sorin Dragomir |
| Publisher | : Springer |
| Total Pages | : 402 |
| Release | : 2016-05-31 |
| Genre | : Mathematics |
| ISBN | : 9811009163 |
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This book gathers contributions by respected experts on the theory of isometric immersions between Riemannian manifolds, and focuses on the geometry of CR structures on submanifolds in Hermitian manifolds. CR structures are a bundle theoretic recast of the tangential Cauchy–Riemann equations in complex analysis involving several complex variables. The book covers a wide range of topics such as Sasakian geometry, Kaehler and locally conformal Kaehler geometry, the tangential CR equations, Lorentzian geometry, holomorphic statistical manifolds, and paraquaternionic CR submanifolds. Intended as a tribute to Professor Aurel Bejancu, who discovered the notion of a CR submanifold of a Hermitian manifold in 1978, the book provides an up-to-date overview of several topics in the geometry of CR submanifolds. Presenting detailed information on the most recent advances in the area, it represents a useful resource for mathematicians and physicists alike.
From Riemann to Differential Geometry and Relativity
| Author | : Lizhen Ji |
| Publisher | : Springer |
| Total Pages | : 647 |
| Release | : 2017-10-03 |
| Genre | : Mathematics |
| ISBN | : 3319600397 |
Download From Riemann to Differential Geometry and Relativity Book in PDF, ePub and Kindle
This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann’s ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann’s work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.
Riemannian Geometry
| Author | : Isaac Chavel |
| Publisher | : Cambridge University Press |
| Total Pages | : 4 |
| Release | : 2006-04-10 |
| Genre | : Mathematics |
| ISBN | : 1139452576 |
Download Riemannian Geometry Book in PDF, ePub and Kindle
This book provides an introduction to Riemannian geometry, the geometry of curved spaces, for use in a graduate course. Requiring only an understanding of differentiable manifolds, the author covers the introductory ideas of Riemannian geometry followed by a selection of more specialized topics. Also featured are Notes and Exercises for each chapter, to develop and enrich the reader's appreciation of the subject. This second edition, first published in 2006, has a clearer treatment of many topics than the first edition, with new proofs of some theorems and a new chapter on the Riemannian geometry of surfaces. The main themes here are the effect of the curvature on the usual notions of classical Euclidean geometry, and the new notions and ideas motivated by curvature itself. Completely new themes created by curvature include the classical Rauch comparison theorem and its consequences in geometry and topology, and the interaction of microscopic behavior of the geometry with the macroscopic structure of the space.
