Moving Frames

Download or read book From Frenet to Cartan: The Method of Moving Frames written by Jeanne N. Clelland and published by American Mathematical Soc.. This book was released on 2017-03-29 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of moving frames originated in the early nineteenth century with the notion of the Frenet frame along a curve in Euclidean space. Later, Darboux expanded this idea to the study of surfaces. The method was brought to its full power in the early twentieth century by Elie Cartan, and its development continues today with the work of Fels, Olver, and others. This book is an introduction to the method of moving frames as developed by Cartan, at a level suitable for beginning graduate students familiar with the geometry of curves and surfaces in Euclidean space. The main focus is on the use of this method to compute local geometric invariants for curves and surfaces in various 3-dimensional homogeneous spaces, including Euclidean, Minkowski, equi-affine, and projective spaces. Later chapters include applications to several classical problems in differential geometry, as well as an introduction to the nonhomogeneous case via moving frames on Riemannian manifolds. The book is written in a reader-friendly style, building on already familiar concepts from curves and surfaces in Euclidean space. A special feature of this book is the inclusion of detailed guidance regarding the use of the computer algebra system Maple™ to perform many of the computations involved in the exercises.

Download or read book Moving Frames written by Carrie Collenberg-González and published by Berghahn Books. This book was released on 2022-02-14 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the building blocks of moving pictures, photographs have played an integral role in cinema since the dawn of the medium—a relationship that has grown more complexly connected even as the underlying technologies continue to evolve. Moving Frames explores the use of photographs in German films from Expressionism to the Berlin School, addressing the formal and narrative roles that photographs play as well as the cultural and historical contexts out of which these films emerged. Looking beyond and within the canon, the editors gather stimulating new insights into the politics of surveillance, resistance, representation, and collective memory functioning through photographic rupture and affect in German cinema.

Download or read book Cartan for Beginners written by Thomas Andrew Ivey and published by American Mathematical Soc.. This book was released on 2003 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to Cartan's approach to differential geometry. Two central methods in Cartan's geometry are the theory of exterior differential systems and the method of moving frames. This book presents thorough and modern treatments of both subjects, including their applications to both classic and contemporary problems. It begins with the classical geometry of surfaces and basic Riemannian geometry in the language of moving frames, along with an elementary introduction to exterior differential systems. Key concepts are developed incrementally with motivating examples leading to definitions, theorems, and proofs. Once the basics of the methods are established, the authors develop applications and advanced topics.One notable application is to complex algebraic geometry, where they expand and update important results from projective differential geometry. The book features an introduction to $G$-structures and a treatment of the theory of connections. The Cartan machinery is also applied to obtain explicit solutions of PDEs via Darboux's method, the method of characteristics, and Cartan's method of equivalence. This text is suitable for a one-year graduate course in differential geometry, and parts of it can be used for a one-semester course. It has numerous exercises and examples throughout. It will also be useful to experts in areas such as PDEs and algebraic geometry who want to learn how moving frames and exterior differential systems apply to their fields.

Download or read book Harmonic Maps, Conservation Laws and Moving Frames written by Frédéric Hélein and published by Cambridge University Press. This book was released on 2002-06-13 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description

Download or read book Differential Geometry For Physicists And Mathematicians: Moving Frames And Differential Forms: From Euclid Past Riemann written by Jose G Vargas and published by World Scientific. This book was released on 2014-03-06 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book that the author wishes had been available to him when he was student. It reflects his interest in knowing (like expert mathematicians) the most relevant mathematics for theoretical physics, but in the style of physicists. This means that one is not facing the study of a collection of definitions, remarks, theorems, corollaries, lemmas, etc. but a narrative — almost like a story being told — that does not impede sophistication and deep results.It covers differential geometry far beyond what general relativists perceive they need to know. And it introduces readers to other areas of mathematics that are of interest to physicists and mathematicians, but are largely overlooked. Among these is Clifford Algebra and its uses in conjunction with differential forms and moving frames. It opens new research vistas that expand the subject matter.In an appendix on the classical theory of curves and surfaces, the author slashes not only the main proofs of the traditional approach, which uses vector calculus, but even existing treatments that also use differential forms for the same purpose.

Download or read book Reference Frames written by Jean Kovalevsky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on reference systems is the first comprehensive review of the problem of celestial and terrestrial reference systems and frames. Over 20 years, the importance of this problem emerged slowly as the accuracy of new observational techniques improved. The topic has already been approached in several symposia such as Stresa (1967), Morioka (1971), Perth (1973), Columbus (1975, 1978 and 1985), Kiev (1977) and San Fernando (1978). Two IAU colloquia held in Turin (1974) and in Warsaw (1980) were exclusively devoted to discuss reference systems. During this time, the problem of terrestrial and celestial reference systems has been discussed also in many astronomical and geodetic symposia, but always among other topics. Thus, a review devoted solely to the definition and practical realization of such systems was needed. It is hoped that this book, containing modern comprehensive reviews of important facets of this problem will contribute not only to a better and wider understanding of the mathematics and the physics that are behind the concepts and the realizations, but also to future development in a field that can only expand with the rapidly increasing accuracy of geodetic and astronomical observations. We are pleased to thank all the authors of the book who have enthusiastically agreed to contribute to the book in their field of competence and have gracefully accepted guidance from the editors in the definition of the subject and of the interfaces with other chapters. We thank Prof. Y.

Download or read book Flash 8: The Missing Manual written by E. A. Vander Veer and published by "O'Reilly Media, Inc.". This book was released on 2006-03-22 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Macromedia's Flash 8 is the world's premier program for adding animation to websites. And with the latest version, this popular program becomes more versatile, letting beginning webmasters and expert developers alike create sophisticated web content. But Flash isn't intuitive. And it doesn't come with a manual. Whether you want to learn the basics or unleash the program's true power, Flash 8: The Missing Manual is the ideal instructor. This hands-on guide to today's hottest web design tool is aimed at nondevelopers, and it teaches you how to translate your ideas into great web content. It begins with a solid primer on animation, which helps you get comfortable with the Flash interface. Once you have these basics under your belt, Flash 8: The Missing Manual moves on to advanced animations, including adding special effects and audio, video, and interactivity to your presentations. When you're really feeling steady, the book shows how to use a dollop of ActionScript to customize your content. It then teaches you how to publish your Flash creations for web surfers everywhere to enjoy. Along the way, the book shows you good design principles and helps you avoid elements that can distract or annoy an audience. Author Emily Vander Veer has more than a dozen books to her credit, including titles on web design and scripting--most written for non-technical readers. Her background makes her the perfect author for a straightforward book on a complex subject. She takes Flash 8: The Missing Manual from the basics to the advanced, yet avoids a hasty jump into tough topics that can leave readers confused. Not only will Flash 8: The Missing Manual help you turn a concept into unique, dynamic content, but it will continue to serve as a reference as you develop your website.