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Enviado por Vitocley flag Denunciar. Differential geometry of curves and surfaces “A free translation, with additional material, of a book and a set of notes, both published originally in Portuguese. Englewood Cliffs, New Jersey 1 All rights reserved. No part of this book may be reproduced in any form, Or by any means, without permission in writing from the pUblisher Current printing: Convex Neighborhoods Appendix: Point-Set Topology of Dfierencial Spaces Bibliography and Comments Hints and Answers to Some Exercises Index Preface This book is geometrja introduction to the differential geometry of curves and surfaces, both in its local and global aspects.
Manfreo presentation differs from the traditional ones by a more extensive use of elementary linear algebra and by a certain emphasis placed on hasicgeometrical facts, rather than on machinery or random details.
Geometria diferencial de curvas e superfícies – Manfredo Perdigão do Carmo – Google Books
We have tried to build each chapter of the book around some simple and fundamental idea. Thus, Chapter 2 develops around the concept of geometriz regular surface in R3; when this concept is properly developed, it is prob- ably the best model for differentiable manifolds. Chapter 3 is built on the Gauss normal map and contains a large amount of the local geometry of surfaces in R3.
Chapter 4 unifies the intrinsic geometry of surfaces around the concept of covariant derivative; again, our purpose was to prepare the reader for the basic notion of connection in Riemannian geometry. Finally, in Chapter 5, we use the first and second variations of grometria length to derive some global properties of surfaces. Near the end of Chapter 5 Sec.
Manfredo Geometria Diferencial
To maintain the proper balance between ideas and facts, we have presented a large number of examples that are computed in detail. Further- more, a reasonable supply of exercises is provided. Some factual material of difedencial differential geometry found its place in these exercises.
Hints or answers are given for the exercises that are starred. The prerequisites for reading this book are linear algebra and calculus.
Geometria diferencial de curvas y superficies/ Differential Geometry of the Superficial Curves
From linear algebra, only the most basic concepts are needed, and a v vi Preface standard undergraduate course on the subject should suffice.
From calculus, a certain familiarity with calculus of several variables including the state- ment of the implicit function theorem is expected.
For the reader’s con- venience, we have tried to restrict our cwrmo to R.
Buck, Advancd Calculus, New York: A certain knowledge of differential equations will be useful but it is not required. This book is a free translation, with additional material, of a book and a set of notes, both published originally in Portuguese. Were it not for the enthusiasm and enormous help of Blaine Lawson, this book would geoetria have come into EngliSh. A large part of the translation was done by Leny Cavalcante.
Manfredo do Carmo – Wikipedia, la enciclopedia libre
I am also indebted to my colleagues and students at IMP A for their comments and support. In particular, Elan Lima read part of the Portuguese version and made valuable comments. Robert Gardner, liirgen Kern, Blaine Lawson, and Nolan Wallach read critically the English manuscript and helped me to avoid several mistakes, both in English and Mathematics.
Ray Ogawa prepared the computer pro- grams for some beautiful drawings that appear in the book Figs.
Jerry Kazdan devoted his time generously and literally offered hundreds of suggestions for the improvement of the manuscript. This final form of the book has benefited greatly from manfreso advice. Rio de Janeiro Manfredo P.
Each chapter starts with an introduction that describes the material in the chapter and explains how this material will be used later in the book. For the reader’s convenience, we have used footnotes to point manfreedo the sections or parts thereof that can be omitted on a first reading. Although there is enough material in the book for a full-year course or a topics diferecnialwe tried to make the book suitable for a first course on differential geometry for students with some background in linear algebra and advanced calculus.
For a short one-quarter course 10 weekswe suggest the use of the following material: