Book by Bar, Christian

A sequel to Lectures on Riemann Surfaces (Mathematical Notes, 1966), this volume continues the discussion of the dimensions of spaces of holomorphic cross-sections of complex line bundles over compact Riemann surfaces. Whereas the earlier treatment was limited to results obtainable chiefly by one-dimensional methods, the more detailed analysis presented here requires the use of various properties of Jacobi varieties and of symmetric products of Riemann surfaces, and so serves as a further introduction to these topics as well.The first chapter consists of a rather explicit description of a canonical basis for the Abelian differentials on a marked Riemann surface, and of the description of the canonical meromorphic differentials and the prime function of a marked Riemann surface. Chapter 2 treats Jacobi varieties of compact Riemann surfaces and various subvarieties that arise in determining the dimensions of spaces of holomorphic cross-sections of complex line bundles. In Chapter 3, the author discusses the relations between Jacobi varieties and symmetric products of Riemann surfaces relevant to the determination of dimensions of spaces of holomorphic cross-sections of complex line bundles. The final chapter derives Torelli's theorem following A. Weil, but in an analytical context.Originally published in 1973.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Product Description: This unique book overturns our ideas about non-Euclidean geometry and the fine-structure constant, and attempts to solve long-standing mathematical problems. It describes a general theory of "recursive" hyperbolic functions based on the "Mathematics of Harmony," and the "golden," "silver," and other "metallic" proportions...read more

Product Description: This text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called “arithmetic hyperbolic surfaces”, the eigenfunctions are of arithmetic nature, and one may use analytic tools as well as powerful methods in number theory to study them...read more

Product Description: This is an excellent tract on what is now an extensive subject. The main points are very clearly put; room has even been found for an outline of non-Euclidean geometry, and the expression of co-ordinates of points on an algebraic curve as one-valued functions...read more

Product Description: This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms...read more

Product Description: From the PREFACE TO THE THIRD EDITION. Researches in the non-Euclidean geometries of Bolyai-Lobachévski and Riemann, while renewing the traditional admiration for Euclid, yet emphasize the advantages of a comparative study of pure spherics and plane geometry before similar figures...read more

Product Description: This graduate textbook begins by introducing Tensors and Riemannian Spaces, and then elaborates their application in solving second-order differential equations, and ends with introducing theory of relativity and de Sitter space. Based on 40 years of teaching experience, the author compiles a well-developed collection of examples and exercises to facilitate the reader's learning...read more

Product Description: THE word theory in the title is to be understood in a very non-technical sense. Indeed, apart from the idea of the invariant elements of an elliptic involution on a straight line, no theory is found at all. The purpose of the book is rather to furnish a certain graphical representation of imaginaries under a number of conventions more or less well known...read more

Product Description: From the ‘Introductory Considerations’ of The Plane Geometry of the Point in Point-Space of Four Dimensions, by C. J. Keyser. 1. As is well known, the dimensionality (in Riemann's sense) of any given space depends upon the element chosen for its construction; and in accordance with the Plücker principle of counting constants, any given space may be made to assume any prescribed dimensionality k by merely taking for element a configuration for whose determination within that space k independent data are necessary and sufficient — a configuration, in other words, whose general analytical representation in the given space involves exactly k parameters...read more

Product Description: Daily Mathematics Practice 100 Worksheets This series of workbooks contains several maths worksheet for practice. Find the face values of the underlined digits in the given numbers of 3 digits each.

Product Description: Daily Mathematics Practice 100 Worksheets This series of workbooks contains several maths worksheet for practice. Find the face values of the underlined digits in the given numbers of 6 digits each.

Product Description: Daily Mathematics Practice 100 Worksheets This series of workbooks contains several maths worksheet for practice. Find the face values of the underlined digits in the given numbers of 5 digits each.

Product Description: Daily Mathematics Practice 100 Worksheets This series of workbooks contains several maths worksheet for practice. Find the face values of the underlined digits in the given numbers of 2 digits each.

Product Description: Daily Mathematics Practice 100 Worksheets This series of workbooks contains several maths worksheet for practice. Find the face values of the underlined digits in the given numbers of 7 digits each.

Product Description: Daily Math Multiplication Practice 30 Worksheets This book contains 30 multiplication worksheets for practice with one multiplicand of 4 digits and one multiplier of 1 digit. These maths problems are provided to improve the mathematics skills by frequent practicing of the worksheets provided...read more

Product Description: The book grew from my lecture notes which I have been polishing since 2001. It is designed for a semester-long course in Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalistic.

This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.

Product Description: Although so many books on elementary geometry are continually appearing, no apology need be offered for the publication of the present work. It has nothing in common with the ordinary text-book, except that it deals with the same subject...read more

Product Description: Simple geometric shapes and symbols combine to make the universal, powerful, sacred model Karen French calls Gateway to the Heavens. In this book, French explains the meaning and purpose of these shapes, how they mold our reality and perception of it and how they have a direct bearing on what you are and why you are here...read more

Product Description: In 1884 the schoolteacher Edwin Abbott wrote a slender volume under the pen name "A Square." This work detailed the culture and customs of the residents of a two-dimensional world called Flatland - and in the process it popularized concepts of higher geometry to a Victorian public...read more