Lectures On Differential Geometry
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Lectures on Differential Geometry
Author: Shlomo Sternberg
language: en
Publisher: American Mathematical Soc.
Release Date: 1999
This book is based on lectures given at Harvard University during the academic year 1960-1961. The presentation assumes knowledge of the elements of modern algebra (groups, vector spaces, etc.) and point-set topology and some elementary analysis. Rather than giving all the basic information or touching upon every topic in the field, this work treats various selected topics in differential geometry. The author concisely addresses standard material and spreads exercises throughout the text. His reprint has two additions to the original volume: a paper written jointly with V. Guillemin at the beginning of a period of intense interest in the equivalence problem and a short description from the author on results in the field that occurred between the first and the second printings.
Lectures on Differential Geometry
This book is a set of notes based on lectures delivered by Prof. Su Buchin at Fudan University, Shanghai in 1978 and 1979 to graduate students as well as teachers from other institutions in China. Some selected topics in global differential geometry are dealt with. Certain areas of classical differential geometry based on modern approach are presented in Lectures 1, 3 and 4. Lecture 2 is on integral geometry on the Euclidean plane. It is abridged from W Blaschke's Vorlesungen Ulber Integralgeometrie. In Lecture 5, Cartan's exterior differential forms are introduced. Fruitful applications in this area by Profs S S Chern and C C Hsiung are also discussed.
Lectures on Classical Differential Geometry
Author: Dirk Jan Struik
language: en
Publisher: Courier Corporation
Release Date: 1961-01-01
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.