Автор: Tu, Loring W. Название: Differential Geometry ISBN: 3319550829 ISBN-13(EAN): 9783319550824 Издательство: Springer Цена: 8943.00 р. Наличие на складе: Есть у поставщикаПоставка под заказ. Описание: Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein`s general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory.
Автор: Sharpe Название: Differential Geometry ISBN: 0387947329 ISBN-13(EAN): 9780387947327 Издательство: Springer Цена: 8378.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Cartan geometries were the first examples of connections on a principal bundle. They seem to be almost unknown these days, in spite of the great beauty and
conceptual power they confer on geometry. The aim of the present book is to fill the gap in the literature on differential geometry by the missing notion of Cartan connections.
Although the author had in mind a book accessible to graduate students, potential readers would also include working differential geometers who would like to know more about what
Cartan did, which was to give a notion of "espaces generalises" (= Cartan geometries) generalizing homogeneous spaces (= Klein geometries) in the same way that Riemannian
geometry generalizes Euclidean geometry. In addition, physicists will be interested to see the fully satisfying way in which their gauge theory can be truly regarded as geometry.
Автор: Javier de Lucas, Cristina Sardon Munoz Название: A Guide to Lie Systems with Compatible Geometric Structures ISBN: 1786346974 ISBN-13(EAN): 9781786346971 Издательство: World Scientific Publishing Рейтинг: Цена: 21384.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
The book presents a comprehensive guide to the study of Lie systems from the fundamentals of differential geometry to the development of contemporary research topics. It embraces several basic topics on differential geometry and the study of geometric structures while developing known applications in the theory of Lie systems. The book also includes a brief exploration of the applications of Lie systems to superequations, discrete systems, and partial differential equations.
Offering a complete overview from the topic's foundations to the present, this book is an ideal resource for Physics and Mathematics students, doctoral students and researchers.
Описание: An inviting, intuitive, and visual exploration of differential geometry and formsVisual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton's geometrical methods to provide geometrical explanations of the classical results.
In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss's famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein's field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell's equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan's method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms.
Six of the seven chapters of Act V can be read completely independently from the rest of the book. Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.
Описание: A New Approach to Differential Geometry using Clifford`s Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra.
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