# Search Results for "geometry-part-2"

## Differential Geometry

**Author**: Shiing-Shen Chern,Robert Osserman**Publisher:**American Mathematical Soc.**ISBN:**0821802488**Category:**Mathematics**Page:**443**View:**2703

Contains sections on Complex differential geometry, Partial differential equations, Homogeneous spaces, Relativity)

## Several Complex Variables and Complex Geometry

**Author**: Eric Bedford,John P. D'Angelo,Steven G. Krantz**Publisher:**American Mathematical Soc.**ISBN:**0821814907**Category:**Mathematics**Page:**625**View:**2732

## Differential geometry, Part 2

**Author**: Pure Mathematics Symposium Staff American Mathematical Society**Publisher:**American Mathematical Soc.**ISBN:**9780821867846**Category:****Page:**N.A**View:**5174

## Modern Geometry— Methods and Applications

*Part II: The Geometry and Topology of Manifolds*

**Author**: B.A. Dubrovin,A.T. Fomenko,S.P. Novikov**Publisher:**Springer Science & Business Media**ISBN:**9780387961620**Category:**Mathematics**Page:**432**View:**6720

Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the classical differential geometry of curves and surfaces which were given instead (and still are given in some places) have come gradually to be viewed as anachronisms. However, there has been hitherto no unanimous agreement as to exactly how such courses should be brought up to date, that is to say, which parts of modern geometry should be regarded as absolutely essential to a modern mathematical education, and what might be the appropriate level of abstractness of their exposition. The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University. The subject-matter and level of abstractness of its exposition were dictated by the view that, in addition to the geometry of curves and surfaces, the following topics are certainly useful in the various areas of application of mathematics (especially in elasticity and relativity, to name but two), and are therefore essential: the theory of tensors (including covariant differentiation of them); Riemannian curvature; geodesics and the calculus of variations (including the conservation laws and Hamiltonian formalism); the particular case of skew-symmetric tensors (i. e.

## Methods of Algebraic Geometry in Control Theory: Part II

*Multivariable Linear Systems and Projective Algebraic Geometry*

**Author**: Peter Falb**Publisher:**Springer Science & Business Media**ISBN:**9780817641139**Category:**Mathematics**Page:**390**View:**4604

"Control theory represents an attempt to codify, in mathematical terms, the principles and techniques used in the analysis and design of control systems. Algebraic geometry may, in an elementary way, be viewed as the study of the structure and properties of the solutions of systems of algebraic equations. The aim of this book is to provide access to the methods of algebraic geometry for engineers and applied scientists through the motivated context of control theory" .* The development which culminated with this volume began over twenty-five years ago with a series of lectures at the control group of the Lund Institute of Technology in Sweden. I have sought throughout to strive for clarity, often using constructive methods and giving several proofs of a particular result as well as many examples. The first volume dealt with the simplest control systems (i.e., single input, single output linear time-invariant systems) and with the simplest algebraic geometry (i.e., affine algebraic geometry). While this is quite satisfactory and natural for scalar systems, the study of multi-input, multi-output linear time invariant control systems requires projective algebraic geometry. Thus, this second volume deals with multi-variable linear systems and pro jective algebraic geometry. The results are deeper and less transparent, but are also quite essential to an understanding of linear control theory. A review of * From the Preface to Part 1. viii Preface the scalar theory is included along with a brief summary of affine algebraic geometry (Appendix E).

## Elements of Descriptive Geometry

**Author**: Lewis Olof Johnson,Irwin Wladaver**Publisher:**N.A**ISBN:**N.A**Category:**Geometry, Descriptive**Page:**N.A**View:**7644

## A.D. Alexandrov

*Selected Works Part II: Intrinsic Geometry of Convex Surfaces*

**Author**: S.S. Kutateladze**Publisher:**CRC Press**ISBN:**9780203643846**Category:**Mathematics**Page:**444**View:**9659

A.D. Alexandrov is considered by many to be the father of intrinsic geometry, second only to Gauss in surface theory. That appraisal stems primarily from this masterpiece--now available in its entirely for the first time since its 1948 publication in Russian. Alexandrov's treatise begins with an outline of the basic concepts, definitions, and results relevant to intrinsic geometry. It reviews the general theory, then presents the requisite general theorems on rectifiable curves and curves of minimum length. Proof of some of the general properties of the intrinsic metric of convex surfaces follows. The study then splits into two almost independent lines: further exploration of the intrinsic geometry of convex surfaces and proof of the existence of a surface with a given metric. The final chapter reviews the generalization of the whole theory to convex surfaces in the Lobachevskii space and in the spherical space, concluding with an outline of the theory of nonconvex surfaces. Alexandrov's work was both original and extremely influential. This book gave rise to studying surfaces "in the large," rejecting the limitations of smoothness, and reviving the style of Euclid. Progress in geometry in recent decades correlates with the resurrection of the synthetic methods of geometry and brings the ideas of Alexandrov once again into focus. This text is a classic that remains unsurpassed in its clarity and scope.