Differential Geometry

Author: Erwin Kreyszig
Publisher: Courier Corporation
ISBN: 9780486318622
Release Date: 2013-04-26
Genre: Mathematics

An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations.

Differentialgeometrie von Kurven und Fl chen

Author: Manfredo P. do Carmo
Publisher: Springer-Verlag
ISBN: 9783322850720
Release Date: 2013-04-17
Genre: Technology & Engineering

Inhalt: Kurven - Reguläre Flächen - Die Geometrie der Gauß-Abbildung - Die innere Geometrie von Flächen - Anhang

Differential Geometry of Curves and Surfaces

Author: Manfredo P. do Carmo
Publisher: Courier Dover Publications
ISBN: 9780486806990
Release Date: 2016-12-14
Genre: Mathematics

One of the most widely used texts in its field, this volume introduces the differential geometry of curves and surfaces in both local and global aspects. The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details. Many examples and exercises enhance the clear, well-written exposition, along with hints and answers to some of the problems. The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the Gauss map, the intrinsic geometry of surfaces, and global differential geometry. Suitable for advanced undergraduates and graduate students of mathematics, this text's prerequisites include an undergraduate course in linear algebra and some familiarity with the calculus of several variables. For this second edition, the author has corrected, revised, and updated the entire volume.

Lectures on Classical Differential Geometry

Author: Dirk Jan Struik
Publisher: Courier Corporation
ISBN: 0486656098
Release Date: 1961
Genre: Mathematics

Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student. Written by a noted mathematician and historian of mathematics, this volume presents the fundamental conceptions of the theory of curves and surfaces and applies them to a number of examples. Dr. Struik has enhanced the treatment with copious historical, biographical, and bibliographical references that place the theory in context and encourage the student to consult original sources and discover additional important ideas there. For this second edition, Professor Struik made some corrections and added an appendix with a sketch of the application of Cartan's method of Pfaffians to curve and surface theory. The result was to further increase the merit of this stimulating, thought-provoking text — ideal for classroom use, but also perfectly suited for self-study. In this attractive, inexpensive paperback edition, it belongs in the library of any mathematician or student of mathematics interested in differential geometry.

Differential Geometry

Author: Heinrich W. Guggenheimer
Publisher: Courier Corporation
ISBN: 9780486157207
Release Date: 2012-04-27
Genre: Mathematics

This text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; more. Includes exercises and 62 figures.

An Introduction to Differential Geometry

Author: T. J. Willmore
Publisher: Courier Corporation
ISBN: 9780486282107
Release Date: 2013-05-13
Genre: Mathematics

This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.

Differentialgeometrie

Author: Wolfgang Kühnel
Publisher: Springer-Verlag
ISBN: 9783834896551
Release Date: 2010-04-14
Genre: Mathematics

Dieses Buch ist eine Einführung in die Differentialgeometrie. Zunächst geht es um die klassischen Aspekte wie die Geometrie von Kurven und Flächen, bevor dann höherdimensionale Flächen sowie abstrakte Mannigfaltigkeiten betrachtet werden. Die Nahtstelle ist dabei das zentrale Kapitel "Die innere Geometrie von Flächen". Dieses führt den Leser bis hin zu dem berühmten Satz von Gauß-Bonnet, der ein entscheidendes Bindeglied zwischen lokaler und globaler Geometrie darstellt. Die zweite Hälfte des Buches ist der Riemannschen Geometrie gewidmet. Den Abschluss bildet ein Kapitel über "Einstein-Räume", die eine große Bedeutung sowohl in der "Reinen Mathematik" als auch in der Allgemeinen Relativitätstheorie von A. Einstein haben. Es wird großer Wert auf Anschaulichkeit gelegt, was durch zahlreiche Abbildungen unterstützt wird. Im Laufe der Neuauflagen wurde der Text erweitert, neue Aufgaben wurden hinzugefügt und am Ende des Buches wurden zusätzliche Hinweise zur Lösung der Übungsaufgaben ergänzt. Der Text wurde für die fünfte Auflage gründlich durchgesehen und an einigen Stellen verbessert.

Differential Geometry

Author: William C. Graustein
Publisher: Courier Corporation
ISBN: 9780486153230
Release Date: 2012-04-19
Genre: Mathematics

This first course in differential geometry presents the fundamentals of the metric differential geometry of curves and surfaces in a Euclidean space of 3 dimensions, using vector notation and technique. Nearly 200 problems.1935 edition.

Differential Geometric Structures

Author: Walter A. Poor
Publisher: Courier Corporation
ISBN: 9780486151915
Release Date: 2015-04-27
Genre: Mathematics

This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.

Differential Geometry

Author: K. L. Wardle
Publisher: Courier Corporation
ISBN: 9780486462721
Release Date: 2008
Genre: Mathematics

Elementary account covers curvature and torsion, involutes and evolutes, curves on a surface, curvature of surfaces, and developable and ruled surfaces. Numerous problems include complete solutions. 1965 edition.

A Treatise on the Differential Geometry of Curves and Surfaces

Author: Luther Pfahler Eisenhart
Publisher: Courier Corporation
ISBN: 9780486159461
Release Date: 2013-04-25
Genre: Mathematics

Created especially for graduate students by a leading writer on mathematics, this introduction to the geometry of curves and surfaces concentrates on problems that students will find most helpful.

Lectures on Classical Differential Geometry

Author: Dirk J. Struik
Publisher: Courier Corporation
ISBN: 9780486138183
Release Date: 2012-04-26
Genre: Mathematics

Excellent brief introduction presents fundamental theory of curves and surfaces and applies them to a number of examples. Topics include curves, theory of surfaces, fundamental equations, envelopes, more. Many problems and solutions. Bibliography.

Differential Geometry

Author: Heinrich Walter Guggenheimer
Publisher: Dover Books on Mathematics
ISBN: 0486634337
Release Date: 1977
Genre: Mathematics

This text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; more. Includes exercises and 62 figures.