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Metric affine geometry

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Published by Dover Publications in New York .
Written in English

Subjects:

  • Geometry, Affine.,
  • Vector spaces.

Book details:

Edition Notes

Statementby Ernst Snapper and Robert J. Troyer.
ContributionsTroyer, Robert J., 1928-
Classifications
LC ClassificationsQA477 .S63 1989
The Physical Object
Paginationxx, 435 p. :
Number of Pages435
ID Numbers
Open LibraryOL2210482M
ISBN 100486661083
LC Control Number89033000

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  Metric Affine Geometry focuses on linear algebra, which is the source for the axiom systems of all affine and projective geometries, both metric and nonmetric. This book is organized into three chapters. Chapter 1 discusses nonmetric affine geometry, while Chapter 2 reviews inner products of vector Edition: 1. The first part of the book deals with the correlation between synthetic geometry and linear algebra. In the second part, geometry is used to introduce lattice theory, and the book culminates with the fundamental theorem of projective geometry. While emphasizing affine geometry and its basis in Euclidean concepts, the book: Builds an Cited by: On the one hand, affine geometry is Euclidean geometry with congruence left out; on the other hand, affine geometry may be obtained from projective geometry by the designation of a particular line or plane to represent the points at infinity. [18] In affine geometry, there is no metric structure but the parallel postulate does hold. Additional Physical Format: Online version: Snapper, Ernst, Metric affine geometry. New York: Dover Publications, , © (OCoLC)

Metric affine geometry. New York, Academic Press [] (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: Ernst Snapper; Robert J Troyer. Metric Affine Geometry focuses on linear algebra, which is the source for the axiom systems of all affine and projective geometries, both metric and nonmetric. This book is organized into three chapters. Chapter 1 discusses nonmetric affine geometry, while Chapter 2 reviews inner products of vector : $ In comparison with General Relativity, dynamic variables of metric-affine gravitation theory are both a pseudo-Riemannian metric and a general linear connection on a world -affine gravitation theory has been suggested as a natural generalization of Einstein–Cartan theory of gravity with torsion where a linear connection obeys the condition that a covariant derivative . The best introduction to affine geometry I know Vectors and Transformations in Plane Geometry by Philippe Tondeur. Using nothing more then vector and matrix algebra in the plane, it develops basic Euclidean geometry with the transformations of similarities and isometries in the plane as completely and clearly as any book I've seen.

Special affine transforms th at maintain the Euclidean metric are similarities; the ratio of any vector norm with respect to the norm of its transformed vector is a datum of a similarity. Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros.. The fundamental objects of study in algebraic geometry are algebraic varieties, which are .   Abstract: “Metric geometry” is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations. Publisher Summary. This chapter focuses on linear connections. Tangent spaces play a key role in differential geometry. The tangent space at a point, x, is the totality of all contravariant vectors, or differentials, associated with that means of an affine connection, the tangent spaces at any two points on a curve are related by an affine transformation, which will, in general.