# krainaksiazek lecture notes on differential geometry 20045783

- znaleziono 5 produktów w 1 sklepie

### Lecture Notes on O-Minimal Structures and Real Analytic Geometry Springer, Berlin

**Książki / Literatura obcojęzyczna**

This volume was produced in conjunction with the Thematic Program in o-Minimal Structures and Real Analytic Geometry, held from January to June of 2009 at the Fields Institute. Five of the six contributions consist of notes from graduate courses associated with the program: Felipe Cano on a new proof of resolution of singularities for planar analytic vector fields; Chris Miller on o-minimality and Hardy fields; Jean-Philippe Rolin on the construction of o-minimal structures from quasianalytic classes; Fernando Sanz on non-oscillatory trajectories of vector fields; and Patrick Speissegger on pfaffian sets. The sixth contribution, by Antongiulio Fornasiero and Tamara Servi, is an adaptation to the nonstandard setting of A.J. Wilkie's construction of o-minimal structures from infinitely differentiable functions. Most of this material is either unavailable elsewhere or spread across many different sources such as research papers, conference proceedings and PhD theses. §This book will be a useful tool for graduate students or researchers from related fields who want to learn about expansions of o-minimal structures by solutions, or images thereof, of definable systems of differential equations. §

Sklep: Libristo.pl

### Global Differential Geometry of Surfaces Springer Netherlands

**Książki / Literatura obcojęzyczna**

Writing this book, I had in my mind areader trying to get some knowledge of a part of the modern differential geometry. I concentrate myself on the study of sur faces in the Euclidean 3-space, this being the most natural object for investigation. The global differential geometry of surfaces in E3 is based on two classical results: (i) the ovaloids (i.e., closed surfaces with positive Gauss curvature) with constant Gauss or mean curvature are the spheres, (ü) two isometrie ovaloids are congruent. The results presented here show vast generalizations of these facts. Up to now, there is only one book covering this area of research: the Lecture Notes [3] written in the tensor slang. In my book, I am using the machinary of E. Cartan's calculus. It should be equivalent to the tensor calculus; nevertheless, using it I get better results (but, honestly, sometimes it is too complicated). It may be said that almost all results are new and belong to myself (the exceptions being the introductory three chapters, the few classical results and results of my post graduate student Mr. M. ÄFWAT who proved Theorems V.3.1, V.3.3 and VIII.2.1-6).

Sklep: Libristo.pl

### Global Differential Geometry of Surfaces Springer Netherlands

**Książki / Literatura obcojęzyczna**

Writing this book, I had in my mind areader trying to get some knowledge of a part of the modern differential geometry. I concentrate myself on the study of sur faces in the Euclidean 3-space, this being the most natural object for investigation. The global differential geometry of surfaces in E3 is based on two classical results: (i) the ovaloids (i.e., closed surfaces with positive Gauss curvature) with constant Gauss or mean curvature are the spheres, (ü) two isometrie ovaloids are congruent. The results presented here show vast generalizations of these facts. Up to now, there is only one book covering this area of research: the Lecture Notes [3] written in the tensor slang. In my book, I am using the machinary of E. Cartan's calculus. It should be equivalent to the tensor calculus; nevertheless, using it I get better results (but, honestly, sometimes it is too complicated). It may be said that almost all results are new and belong to myself (the exceptions being the introductory three chapters, the few classical results and results of my post graduate student Mr. M. ÄFWAT who proved Theorems V.3.1, V.3.3 and VIII.2.1-6).

Sklep: Libristo.pl

### Mathematics of Relativity Lecture Notes (Classic Reprint) Forgotten Books

**Książki / Literatura obcojęzyczna**

Excerpt from Mathematics of Relativity Lecture Notes Old Physics; Motion of a Particle. The Inverse Square Law; Two Pictures of Matter; Vectors, Tensors, Operations; Maxwell's Equations; The Stress-Energy Tensor; General Equations of Motion. The Complete Tensor; New Geometry; Analytic Geometry of Four Dimensions; Axioms of Four-Dimensional Geometry; Tensor Analysis; Complications Resulting From Imaginary Coordinate; Are the Equations of Physics Invariant; Curves in the New Geometry; Special Relativity; Equations of Motion; Lorentz Transformations; Addition of Velocities; Light Corpuscles, or Photons; Electricity and Magnetism in Special Relativity; Curved Space; Curvature of Curves and Surfaces; Generalizations; The Riemann Tensor; Vectors in General Coordinates; Tensors in General Coordinates; Covariant and Contravariant Components; Physical Coordinates as General Coordinates; Curvilinear Coordinates in Curved Space; New Derivation of the Riemann Tensor; Differential Relations for the Riemann Tensor; Geodesics; General Relativity; The Law of Geodesics; Solar System, Symmetry Conditions; Solution of the Field Equations; Equations of Geodesics; Newtonian Motion of a Planet; Relativity Motion of a Planet; Deflection of Light; Shift of Spectral Lines About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Sklep: Libristo.pl

### Teichmüller Theory in Riemannian Geometry Birkhäuser

**Książki / Literatura obcojęzyczna**

These lecture notes are based on the joint work of the author and Arthur Fischer on Teichmiiller theory undertaken in the years 1980-1986. Since then many of our colleagues have encouraged us to publish our approach to the subject in a concise format, easily accessible to a broad mathematical audience. However, it was the invitation by the faculty of the ETH Ziirich to deliver the ETH N achdiplom-Vorlesungen on this material which provided the opportunity for the author to develop our research papers into a format suitable for mathematicians with a modest background in differential geometry. We also hoped it would provide the basis for a graduate course stressing the application of fundamental ideas in geometry. For this opportunity the author wishes to thank Eduard Zehnder and Jiirgen Moser, acting director and director of the Forschungsinstitut fiir Mathematik at the ETH, Gisbert Wiistholz, responsible for the Nachdiplom Vorlesungen and the entire ETH faculty for their support and warm hospitality. This new approach to Teichmiiller theory presented here was undertaken for two reasons. First, it was clear that the classical approach, using the theory of extremal quasi-conformal mappings (in this approach we completely avoid the use of quasi-conformal maps) was not easily applicable to the theory of minimal surfaces, a field of interest of the author over many years. Second, many other active mathematicians, who at various times needed some Teichmiiller theory, have found the classical approach inaccessible to them.

Sklep: Libristo.pl

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