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Author: Jeanne N. Clelland Publisher: American Mathematical Soc. ISBN: 1470429527 Category : Differential geometry -- Classical differential geometry -- Affine differential geometry Languages : en Pages : 414
Book Description
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.
Author: Jeanne N. Clelland Publisher: American Mathematical Soc. ISBN: 1470429527 Category : Differential geometry -- Classical differential geometry -- Affine differential geometry Languages : en Pages : 414
Book Description
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.
Author: Thomas Andrew Ivey Publisher: American Mathematical Soc. ISBN: 0821833758 Category : Mathematics Languages : en Pages : 394
Book Description
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.
Author: Carrie Collenberg-González Publisher: Berghahn Books ISBN: 1800733763 Category : History Languages : en Pages : 0
Book Description
Introduction. Photographs as rupture and affect in German film / Carrie Collenberg-González and Martin P. Sheehan -- Layers of exposure : the photographic approach in Gerhart Lamprecht's Zille film, Slums of Berlin (1925) / Jason Doerre -- Objecting objects : photographs and subjectivity in The blue angel (1930) / Martin P. Sheehan -- Before- and afterlives : on the stillness of photographs at the outset of Adenauer cinema / John Davidson -- Filming after Walker Evans : Wim Wenders' "American pictures" in Kings of the road (1976) / Stefanie Harris -- The transgression of overpainting : Jürgen Böttcher's radical experiments with intermediality in Transformations (1981) / Matthew Bauman -- The promise of agency : photographs and value in Tattoo (2002) / Cynthia Porter -- Curating the image : visual intertextuality in The Baader Meinhof Complex (2008) / Reinhard Zachau -- Re-presenting German heritage films : photographic memory in Aimee & Jaguar (1999), Good bye Lenin! (2003), and Almanya-Welcome to Germany (2011) / Carrie Collenberg-Gonzalez -- Imaging the "good life" : destabilizing subjecthood and conceptions of the normative family in Ghosts (2005) / Simone Pfleger -- Violence, death, and photographs : capturing the (un)dead in Rammbock (2010) / Melissa Etzler -- Possible archives : encountering a surveillance photo in Karl Marx City (2016) / Anke Pinkert -- Afterword. Toward a camera ludica : agency and photography in Videogame ecologies / Curtis L. Maughan.
Author: Carrie Collenberg-González Publisher: Berghahn Books ISBN: 1800733771 Category : Performing Arts Languages : en Pages : 257
Book Description
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.
Author: José G Vargas Publisher: World Scientific ISBN: 9814566411 Category : Science Languages : en Pages : 312
Book Description
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. Contents:Introduction:OrientationsTools:Differential FormsVector Spaces and Tensor ProductsExterior DifferentiationTwo Klein Geometries:Affine Klein GeometryEuclidean Klein GeometryCartan Connections:Generalized Geometry Made SimpleAffine ConnectionsEuclidean ConnectionsRiemannian Spaces and Pseudo-SpacesThe Future?:Extensions of CartanUnderstand the Past to Imagine the FutureA Book of Farewells Readership: Physicists and mathematicians working on differential geometry. Keywords:Differential Geometry;Differential Forms;Moving Frames;Exterior CalculusKey Features:Reader FriendlyNaturalnessRespect for the history of the subject and related incisiveness
Author: G. Rizzi Publisher: Springer Science & Business Media ISBN: 9401705283 Category : Science Languages : en Pages : 456
Book Description
Even if the subject is a long-standing one, this is the first monograph on this field. On the one hand, this book is intended to give a rather wide review on this field, both in a historical and pedagogical perspective; on the other hand, it aims at critically re-examining and discussing the most controversial issues. For instance, according to some authors the celebrated Sagnac effect is a disproval of the theory of relativity applied to rotating frames; according to others, it is an astonishing experimental evidence of the relativistic theory. In order to give the reader a deeper insight into this research field, the contributing authors discuss their opinions on the main subjects in an enthralling virtual round table: in this way, the reader can get a direct comparison of the various viewpoints on the most controversial and interesting topics. This is particularly expedient, since the differences in the various approaches are often based upon subtleties that can be understood only by a direct comparison of the underlying hypotheses.
Author: Jean Kovalevsky Publisher: Springer Science & Business Media ISBN: 9400909330 Category : Science Languages : en Pages : 470
Book Description
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.
Author: V. Cappellini Publisher: Elsevier ISBN: 9780080543062 Category : Computers Languages : en Pages : 332
Book Description
New digital image processing and recognition methods, implementation techniques and advanced applications (television, remote sensing, biomedicine, traffic, inspection, robotics, etc.) are presented in this volume. Novel approaches (i.e. digital filters, source coding, neural networks etc.) for solving 2-D and 3-D problems are described. Many papers focus on the motion estimation and tracking recognition of moving objects. The increasingly important field of Cultural Heritage is also covered. Some papers are more theoretical or of review nature, while others contain new implementations and applications. Generally the book presents - for the above outlined area - the state of the art (theory, implementation, applications) with future trends. This book will be of interest not only to researchers, professors and students in university departments of engineering, communications, computers and automatic control, but also to engineers and managers of industries concerned with computer vision, manufacturing, automation, robotics and quality control.
Author: Dieter Strauch Publisher: Springer Science & Business Media ISBN: 3540736166 Category : Science Languages : en Pages : 414
Book Description
This upper-level undergraduate and beginning graduate textbook primarily covers the theory and application of Newtonian and Lagrangian, but also of Hamiltonian mechanics. In addition, included are elements of continuum mechanics and the accompanying classical field theory, wherein four-vector notation is introduced without explicit reference to special relativity. The author's writing style attempts to ease students through the primary and secondary results, thus building a solid foundation for understanding applications. Numerous examples illustrate the material and often present alternative approaches to the final results.
Author: Jeanne N. Clelland
Author: Jeanne N. Clelland
Author: Thomas Andrew Ivey
Author: Carrie Collenberg-González
Author: Frédéric Hélein
Author: Carrie Collenberg-González
Author: José G Vargas
Author: G. Rizzi
Author: Jean Kovalevsky
Author: V. Cappellini
Author: Dieter Strauch