C Projective Geometry
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C Projective Geometry
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Author : David M Calderbank
language : en
Publisher: American Mathematical Society
Release Date : 2021-02-10
C Projective Geometry written by David M Calderbank and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-10 with Mathematics categories.
The authors develop in detail the theory of (almost) c-projective geometry, a natural analogue of projective differential geometry adapted to (almost) complex manifolds. The authors realise it as a type of parabolic geometry and describe the associated Cartan or tractor connection. A Kähler manifold gives rise to a c-projective structure and this is one of the primary motivations for its study. The existence of two or more Kähler metrics underlying a given c-projective structure has many ramifications, which the authors explore in depth. As a consequence of this analysis, they prove the Yano–Obata Conjecture for complete Kähler manifolds: if such a manifold admits a one parameter group of c-projective transformations that are not affine, then it is complex projective space, equipped with a multiple of the Fubini-Study metric.
Projective Geometry
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Author : Boyd C. Patterson
language : en
Publisher:
Release Date : 1954
Projective Geometry written by Boyd C. Patterson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1954 with categories.
Lectures In Projective Geometry
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Author : A. Seidenberg
language : en
Publisher: Courier Corporation
Release Date : 2012-06-14
Lectures In Projective Geometry written by A. Seidenberg and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-14 with Mathematics categories.
An ideal text for undergraduate courses, this volume takes an axiomatic approach that covers relations between the basic theorems, conics, coordinate systems and linear transformations, quadric surfaces, and the Jordan canonical form. 1962 edition.
The Real Projective Plane
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Author : H.S.M. Coxeter
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Real Projective Plane written by H.S.M. Coxeter 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 2012-12-06 with Mathematics categories.
Along with many small improvements, this revised edition contains van Yzeren's new proof of Pascal's theorem (§1.7) and, in Chapter 2, an improved treatment of order and sense. The Sylvester-Gallai theorem, instead of being introduced as a curiosity, is now used as an essential step in the theory of harmonic separation (§3.34). This makes the logi cal development self-contained: the footnotes involving the References (pp. 214-216) are for comparison with earlier treatments, and to give credit where it is due, not to fill gaps in the argument. H.S.M.C. November 1992 v Preface to the Second Edition Why should one study the real plane? To this question, put by those who advocate the complex plane, or geometry over a general field, I would reply that the real plane is an easy first step. Most of the prop erties are closely analogous, and the real field has the advantage of intuitive accessibility. Moreover, real geometry is exactly what is needed for the projective approach to non· Euclidean geometry. Instead of introducing the affine and Euclidean metrics as in Chapters 8 and 9, we could just as well take the locus of 'points at infinity' to be a conic, or replace the absolute involution by an absolute polarity.
Complex Projective Geometry
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Author : Geir Ellingsrud
language : en
Publisher:
Release Date : 2014-05-14
Complex Projective Geometry written by Geir Ellingsrud and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with Algebraic varieties categories.
A volume of papers describing new methods in algebraic geometry.
Complex Projective Geometry
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Author : G. Ellingsrud
language : en
Publisher:
Release Date : 1992
Complex Projective Geometry written by G. Ellingsrud and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Algebraic varieties categories.
A volume of papers describing new methods in algebraic geometry.
Foundations Of Geometry
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Author : Karol Borsuk
language : en
Publisher: Courier Dover Publications
Release Date : 2018-11-14
Foundations Of Geometry written by Karol Borsuk and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-14 with Mathematics categories.
In Part One of this comprehensive and frequently cited treatment, the authors develop Euclidean and Bolyai-Lobachevskian geometry on the basis of an axiom system due, in principle, to the work of David Hilbert. Part Two develops projective geometry in much the same way. An Introduction provides background on topological space, analytic geometry, and other relevant topics, and rigorous proofs appear throughout the text. Topics covered by Part One include axioms of incidence and order, axioms of congruence, the axiom of continuity, models of absolute geometry, and Euclidean geometry, culminating in the treatment of Bolyai-Lobachevskian geometry. Part Two examines axioms of incidents and order and the axiom of continuity, concluding with an exploration of models of projective geometry.
Notes On Geometry
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Author : Elmer G. Rees
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Notes On Geometry written by Elmer G. Rees 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 2012-12-06 with Mathematics categories.
In recent years, geometry has played a lesser role in undergraduate courses than it has ever done. Nevertheless, it still plays a leading role in mathematics at a higher level. Its central role in the history of mathematics has never been disputed. It is important, therefore, to introduce some geometry into university syllabuses. There are several ways of doing this, it can be incorporated into existing courses that are primarily devoted to other topics, it can be taught at a first year level or it can be taught in higher level courses devoted to differential geometry or to more classical topics. These notes are intended to fill a rather obvious gap in the literature. It treats the classical topics of Euclidean, projective and hyperbolic geometry but uses the material commonly taught to undergraduates: linear algebra, group theory, metric spaces and complex analysis. The notes are based on a course whose aim was two fold, firstly, to introduce the students to some geometry and secondly to deepen their understanding of topics that they have already met. What is required from the earlier material is a familiarity with the main ideas, specific topics that are used are usually redone.
Projective Geometry
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Author : H.S.M. Coxeter
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-10-09
Projective Geometry written by H.S.M. Coxeter 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 2003-10-09 with Mathematics categories.
In Euclidean geometry, constructions are made with ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything, instead, one relates one set of points to another by a projectivity. The first two chapters of this book introduce the important concepts of the subject and provide the logical foundations. The third and fourth chapters introduce the famous theorems of Desargues and Pappus. Chapters 5 and 6 make use of projectivities on a line and plane, respectively. The next three chapters develop a self-contained account of von Staudt's approach to the theory of conics. The modern approach used in that development is exploited in Chapter 10, which deals with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The concluding chapters show the connections among projective, Euclidean, and analytic geometry.
Projective Geometry
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Author : Oswald Veblen
language : en
Publisher: Rarebooksclub.com
Release Date : 2013-09
Projective Geometry written by Oswald Veblen and has been published by Rarebooksclub.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09 with categories.
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1910 edition. Excerpt: ...The coordinates of a double point (xv x) must satisfy the equations pxi = ax1 + bx2, px = cx1 + dxr These equations are compatible only if the determinant of the system 3 (a-p)c1+bx2=0, cxl+(d-p)x =0, vanishes. This leads to the equation a-p b I' c d--p for the determination of the factor of proportionality p. This equation is called the characteristic equation of the matrix representing the projectivity. Every value of p satisfying this equation then leads to a double point when substituted in one of the equations (3); viz., if p, be a solution of the characteristic equation, the point (xv ag = (-b, a-pl) = (d-pv-c) is a double point. In homogeneous coordinates the cross ratio R (AB, CD) of four points A = (av a3), B = (bv ft2), C = (cv c2), D = (dv d ) is given by (ac) (be) (ad) ' (bd)' where the expressions (ac), etc., are used as abbreviations for a--a, etc. This statement is readily verified by writing down the above ratio in terms of the nonhomogeneous coordinates of the four points. We will close this section by giving to the two homogeneous coordinates of a point on a line an explicit geometrical significance. In view of the fact that the coordinates of such a point are not uniquely determined, a factor of proportionality being entirely arbitrary, there may be many such interpretations. On account of the existence of this arbitrary factor, we may impose a further condition on the coordinates (xv x2) of a point, in addition to the defining relation x1/x2=x, where x is the nonhomogeneous coordinate of the point in question. We choose the relation x1 + x2 = 1. If this relation is satisfied, Thus homogeneous coordinates subject to the condition xl+x2 = l can be defined by choosing three points A, B, C arbitrarily, ...