We consider Levi non-degenerate tube hypersurfaces in complex linear space which are "spherical," that is, locally CR-equivalent to the real hyperquadric. Spherical hypersurfaces are characterized by the condition of the vanishing of the CR-curvature form, so such hypersurfaces are flat from the CR-geometric viewpoint. On the other hand, such hypersurfaces are of interest from the point of view of affine geometry.
Thus our treatment of spherical tube hypersurfaces in this book is two-fold: CR-geometric and affine-geometric. Spherical tube hypersurfaces turn out to possess remarkable properties. For example, every such hypersurface is real-analytic and extends to a closed real-analytic spherical tube hypersurface in complex space. One of our main goals is to give an explicit affine classification of closed spherical tube hypersurfaces whenever possible. In this book we offer a comprehensive exposition of the theory of spherical tube hypersurfaces starting with the idea proposed in the pioneering work by P.
Yang and ending with the new approach due to G. Fels and W. Kaup This distinctive text will prove most rewarding for students who have a genuine passion for mathematics as well as certain mathematical maturity. Primarily aimed at undergraduates with working knowledge of real analysis and metric spaces, this book can also be used to instruct a graduate course. The text uses a conversational style with topics purposefully apportioned into 21 lectures, providing a suitable format for either independent study or lecture-based teaching.
Instructors are invited to rearrange the order of topics according to their own vision. A clear and rigorous exposition is supported by engaging examples and exercises unique to each lecture; a large number of exercises contain useful calculation problems. Hints are given for a selection of the more difficult exercises. In addition to its primary purpose as a textbook for a formal course, however, it is the authors' hope that this book will also prove of value to readers interested in studying mathematical analysis on their own.
Indeed, we believe the wealth and variety of examples and exercises will be especially conducive to this end. A word on prerequisites. With what mathematical background might a prospective reader hope to profit from the study of this book? Our con scious intent in writing it was to address the needs of a beginning graduate student in mathematics, or, to put matters slightly differently, a student who has completed an undergraduate program with a mathematics ma jor.
On the other hand, the book is very largely self-contained and should therefore be accessible to a lower classman whose interest in mathematical analysis has already been awakened.
Lars V. Contributions to Analysis: A Collection of Papers Dedicated to Lipman Bers is a compendium of papers provided by Bers, friends, students, colleagues, and professors.
These papers deal with Teichmuller spaces, Kleinian groups, theta functions, algebraic geometry. Other papers discuss quasiconformal mappings, function theory, differential equations, and differential topology. One paper discusses the results of the rigidity theorem of Mostow and its generalization by Marden in relation to geometric properties of Kleinian groups of the first kind. These results, obtained by planar methods, are presented in terms of the hyperbolic 3-space language, which is a natural pedestal in approaching the action of the Kleinian groups.
Another paper reviews Riemann's vanishing theorem which solves the Jacobi inversion problem, by relating the vanishing properties of the theta function particularly at half periods to properties of certain linear series on the Riemann surface. One paper examines the problem of obtaining relations among the periods of the differentials of first kind on a compact Riemann surface.
An application of a computer program involves supersonic transport. The program is based on the hodograph transformation and a method of complex characteristics to calculate profiles that are shock-less at a specified angle of attack, or at a specified subsonic free-stream Mach number. The collection can prove useful for engineers, statisticians, students, and professors in advance mathematics or courses related to aeronautics. Practical Analysis in One Variable. Donald Estep. Background I was an eighteen-year-old freshman when I began studying analysis. I had arrived at Columbia University ready to major in physics or perhaps engineering.
Then after the course was over, Professor Bers called me into his o? He told me that if I could read this book over the summer,understandmostofit,andproveitbydoingmostoftheproblems, then I might have a career as a mathematician. In school, I restlessly wandered through complex analysis, analyticnumbertheory,andpartialdi?
But underlying all of this indecision was an ever-present and ever-growing appreciation of analysis. An appreciation thatstillsustainsmyintellectevenintheoftencynicalworldofthemodern academic professional.
But developing this appreciation did not come easy to me, and the p- sentation in this book is motivated by my struggles to understand the viii Preface most basic concepts of analysis. To paraphrase J. Similar ebooks. Alexander Isaev. Kobayashi-hyperbolic manifolds are an object of active research in complex geometry. In this monograph the author presents a coherent exposition of recent results on complete characterization of Kobayashi-hyperbolic manifolds with high-dimensional groups of holomorphic automorphisms.
These classification results can be viewed as complex-geometric analogues of those known for Riemannian manifolds with high-dimensional isotropy groups, that were extensively studied in the ss.
The common feature of the Kobayashi-hyperbolic and Riemannian cases is the properness of the actions of the holomorphic automorphism group and the isometry group on respective manifolds. Calculus For Dummies: Edition 2. Mark Ryan. While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. Slay the calculus monster with this user-friendly guide Calculus For Dummies, 2nd Edition makes calculus manageable—even if you're one of the many students who sweat at the thought of it.
The book is written in a clear style, and almost all proofs are carried out in detail.
Even auxiliary parts from other fields are explained and sometimes proved. This underlines in addition, how close this field is to the broad flow of modern mathematics. It is written in such a way that it can be used as an introduction to affine differential geometry, but also as a handbook for experts. Since then everyone interested in affine differential geometry has been indebted to the authors.
They wrote an excellent book from elementary aspects up to then- recent research. In the new edition, they include some significant developments of the last two decades.
This monograph also contains some historical aspects of the development of the affine differential geometry in the introduction and also in each chapter , interesting and useful at the same time. It is obvious that the authors succeeded to present in this book new results, but also important global methods in affine differential geometry. Their expertise in this area of research has a major contribution in making this monograph, in the reviewer's opinion, one of the best actual and modern books in affine differential geometry.