Differential geometry : curves  surfaces  manifolds
 Uniform Title
 Differentialgeometrie. English
 Author/Creator
 Kühnel, Wolfgang, 1950
 Language
 English.
 Edition
 2nd ed.
 Imprint
 Providence, R.I. : American Mathematical Society, c2006.
 Physical description
 xii, 380 p. : ill. ; 22 cm.
 Series
 Student mathematical library ; v. 16.
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QA641 .K9613 2006
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. 367370) and index.
 Contents

 Notations and prerequisites from analysis Curves in $I\!\!R^n$ The local theory of surfaces The intrinsic geometry of surfaces Riemannian manifolds The curvature tensor Spaces of constant curvature Einstein spaces Bibliography List of notation Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 Our first knowledge of differential geometry usually comes from the study of the curves and surfaces in $I\!\!R^3$ that arise in calculus. Here we learn about line and surface integrals, divergence and curl, and the various forms of Stokes' Theorem. If we are fortunate, we may encounter curvature and such things as the SerretFrenet formulas. With just the basic tools from multivariable calculus, plus a little knowledge of linear algebra, it is possible to begin a much richer and rewarding study of differential geometry, which is what is presented in this book. It starts with an introduction to the classical differential geometry of curves and surfaces in Euclidean space, then leads to an introduction to the Riemannian geometry of more general manifolds, including a look at Einstein spaces. An important bridge from the lowdimensional theory to the general case is provided by a chapter on the intrinsic geometry of surfaces.The first half of the book, covering the geometry of curves and surfaces, would be suitable for a onesemester undergraduate course. The local and global theories of curves and surfaces are presented, including detailed discussions of surfaces of rotation, ruled surfaces, and minimal surfaces. The second half of the book, which could be used for a more advanced course, begins with an introduction to differentiable manifolds, Riemannian structures, and the curvature tensor. Two special topics are treated in detail: spaces of constant curvature and Einstein spaces.The main goal of the book is to get started in a fairly elementary way, then to guide the reader toward more sophisticated concepts and more advanced topics. There are many examples and exercises to help along the way. Numerous figures help the reader visualize key concepts and examples, especially in lower dimensions. For the second edition, a number of errors were corrected and some text and a number of figures have been added.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2006
 Responsibility
 Wolfgang Kühnel ; translated by Bruce Hunt.
 Series
 Student mathematical library, 15209121 ; v. 16
 ISBN
 0821839888
 9780821839881