Differential Geometric Structures

Author: Walter A. Poor

Publisher: Courier Corporation

ISBN: 0486151913

Category: Mathematics

Page: 352

View: 1292

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: Erwin Kreyszig

Publisher: Courier Corporation

ISBN: 9780486667218

Category: Mathematics

Page: 352

View: 5458

Text from preface: "This book provides an introduction to the differential geometry of curves and surfaces in three-dimensional Euclidean space"


Kurven - Flächen - Mannigfaltigkeiten

Author: Wolfgang Kühnel

Publisher: Springer-Verlag

ISBN: 3658006153

Category: Mathematics

Page: 284

View: 3884

Dieses Buch ist eine Einführung in die Differentialgeometrie und ein passender Begleiter zum Differentialgeometrie-Modul (ein- und zweisemestrig). 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. Bei der Neuauflage wurden einige zusätzliche Lösungen zu den Übungsaufgaben ergänzt.

Galoissche Theorie

Author: Emil Artin

Publisher: N.A


Category: Galois theory

Page: 86

View: 3924

Differentialgeometrie von Kurven und Flächen

Author: Manfredo P. do Carmo

Publisher: Springer-Verlag

ISBN: 3322850722

Category: Technology & Engineering

Page: 263

View: 8773

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

Differential Forms with Applications to the Physical Sciences

Author: Harley Flanders

Publisher: Courier Corporation

ISBN: 0486139611

Category: Mathematics

Page: 240

View: 2489

A graduate-level text utilizing exterior differential forms in the analysis of a variety of mathematical problems in the physical and engineering sciences. Includes 45 illustrations. Index.

Introduction to Differential Geometry for Engineers

Author: Brian F. Doolin,Clyde F. Martin

Publisher: Courier Corporation

ISBN: 0486281949

Category: Mathematics

Page: 176

View: 5422

This outstanding guide supplies important mathematical tools for diverse engineering applications, offering engineers the basic concepts and terminology of modern global differential geometry. Suitable for independent study as well as a supplementary text for advanced undergraduate and graduate courses, this volume also constitutes a valuable reference for control, systems, aeronautical, electrical, and mechanical engineers.The treatment's ideas are applied mainly as an introduction to the Lie theory of differential equations and to examine the role of Grassmannians in control systems analysis. Additional topics include the fundamental notions of manifolds, tangent spaces, vector fields, exterior algebra, and Lie algebras. An appendix reviews concepts related to vector calculus, including open and closed sets, compactness, continuity, and derivative.

The Ricci Flow: Analytic aspects

Author: Bennett Chow

Publisher: American Mathematical Soc.

ISBN: 0821844296

Category: Mathematics

Page: 458

View: 3190

Geometric analysis has become one of the most important tools in geometry and topology. In their books on the Ricci flow, the authors reveal the depth and breadth of this flow method for understanding the structure of manifolds. With the present book, the authors focus on the analytic aspects of Ricci flow. Some highlights of the presentation are weak and strong maximum principles for scalar heat-type equations and systems on manifolds, the classification by Bohm and Wilking of closed manifolds with 2-positive curvature operator, Bando's result that solutions to the Ricci flow are real analytic in the space variables, Shi's local derivative of curvature estimates and some variants, and differential Harnack estimates of Li-Yau-type including Hamilton's matrix estimate for the Ricci flow and Perelman's estimate for fundamental solutions of the adjoint heat equation coupled to the Ricci flow. The authors have tried to make some advanced material accessible to graduate students and nonexperts. The book gives a rigorous introduction to some of Perelman's work and explains some technical aspects of Ricci flow useful for singularity analysis. They have also attempted to give the appropriate references so that the reader may further pursue the statements and proofs of the various results. Also in the Mathematical Surveys and Monographs series: The Ricci Flow: An Introduction, Bennett Chow and Dan Knopf, Vol. 110, 2004. The Ricci Flow: Techniques and Applications. Part I: Geometric Aspects, Bennett Chow, Sun-Chin Chu, David Glickenstein, Christine Guenther, James Isenberg, Tom Ivey, Dan Knopf, Peng Lu, Feng Luo, and Lei Ni, Vol. 135, 2007. The Ricci Flow: Techniques and Applications. Part III: Geometric-Analytic Aspects, Bennett Chow, Sun-Chin Chu, David Glickenstein, Christine Guenther, James Isenberg, Tom Ivey, Dan Knopf, Peng Lu, Feng Luo, and Lei Ni (forthcoming).

Differential Manifolds

Author: Antoni A. Kosinski

Publisher: Courier Corporation

ISBN: 048631815X

Category: Mathematics

Page: 288

View: 8827

Introductory text for advanced undergraduates and graduate students presents systematic study of the topological structure of smooth manifolds, starting with elements of theory and concluding with method of surgery. 1993 edition.

The Development of Mathematics

Author: E. T. Bell

Publisher: Courier Corporation

ISBN: 0486152286

Category: Mathematics

Page: 656

View: 5728

Time-honored study by a prominent scholar of mathematics traces decisive epochs from the evolution of mathematical ideas in ancient Egypt and Babylonia to major breakthroughs in the 19th and 20th centuries. 1945 edition.

Cohomology and Differential Forms

Author: Izu Vaisman

Publisher: Courier Dover Publications

ISBN: 0486804836

Category: Mathematics

Page: 304

View: 4239

This monograph explores the cohomological theory of manifolds with various sheaves and its application to differential geometry. Based on lectures given by author Izu Vaisman at Romania's University of Iasi, the treatment is suitable for advanced undergraduates and graduate students of mathematics as well as mathematical researchers in differential geometry, global analysis, and topology. A self-contained development of cohomological theory constitutes the central part of the book. Topics include categories and functors, the Čech cohomology with coefficients in sheaves, the theory of fiber bundles, and differentiable, foliated, and complex analytic manifolds. The final chapter covers the theorems of de Rham and Dolbeault-Serre and examines the theorem of Allendoerfer and Eells, with applications of these theorems to characteristic classes and the general theory of harmonic forms.

Lectures on Classical Differential Geometry

Author: Dirk Jan Struik

Publisher: Courier Corporation

ISBN: 9780486656090

Category: Mathematics

Page: 232

View: 8805

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.

Vector Analysis

Author: Louis Brand

Publisher: Courier Corporation

ISBN: 048615484X

Category: Mathematics

Page: 304

View: 5231

This text was designed as a short introductory course to give students the tools of vector algebra and calculus, as well as a brief glimpse into the subjects' manifold applications. 1957 edition. 86 figures.

The Geometry of Kerr Black Holes

Author: Barrett O'Neill

Publisher: Courier Corporation

ISBN: 0486783111

Category: Science

Page: 400

View: 5228

Suitable for advanced undergraduates and graduate students of mathematics as well as for physicists, this unique monograph and self-contained treatment constitutes an introduction to modern techniques in differential geometry. 1995 edition.

Encyclopaedia of Mathematics

Author: Michiel Hazewinkel

Publisher: Springer Science & Business Media

ISBN: 940095994X

Category: Mathematics

Page: 492

View: 3379

Tensor Analysis on Manifolds

Author: Richard L. Bishop,Samuel I. Goldberg

Publisher: Courier Corporation

ISBN: 9780486640396

Category: Mathematics

Page: 280

View: 7265

Striking just the right balance between formal and abstract approaches, this text proceeds from generalities to specifics. Topics include function-theoretical and algebraic aspects, manifolds and integration theory, several important structures, and adaptation to classical mechanics. "First-rate. . . deserves to be widely read." — American Mathematical Monthly. 1980 edition.

An Introductory Course on Differentiable Manifolds

Author: Siavash Shahshahani

Publisher: Courier Dover Publications

ISBN: 0486820823

Category: Mathematics

Page: 368

View: 8817

Based on author Siavash Shahshahani's extensive teaching experience, this volume presents a thorough, rigorous course on the theory of differentiable manifolds. Geared toward advanced undergraduates and graduate students in mathematics, the treatment's prerequisites include a strong background in undergraduate mathematics, including multivariable calculus, linear algebra, elementary abstract algebra, and point set topology. More than 200 exercises offer students ample opportunity to gauge their skills and gain additional insights. The four-part treatment begins with a single chapter devoted to the tensor algebra of linear spaces and their mappings. Part II brings in neighboring points to explore integrating vector fields, Lie bracket, exterior derivative, and Lie derivative. Part III, involving manifolds and vector bundles, develops the main body of the course. The final chapter provides a glimpse into geometric structures by introducing connections on the tangent bundle as a tool to implant the second derivative and the derivative of vector fields on the base manifold. Relevant historical and philosophical asides enhance the mathematical text, and helpful Appendixes offer supplementary material.

Harmonic Analysis on Homogeneous Spaces

Author: Nolan R. Wallach

Publisher: Courier Dover Publications

ISBN: 0486816923

Category: Mathematics

Page: 384

View: 6857

Requiring background in linear algebra and advanced calculus, this text covers representation theory of compact Lie groups with applications to topology, geometry, and analysis and non-compact semi-simple Lie groups. 1973 edition.