Geometric Mechanics on Riemannian Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Mechanics on Riemannian Manifolds write by Ovidiu Calin. This book was released on 2006-03-15. Geometric Mechanics on Riemannian Manifolds available in PDF, EPUB and Kindle. * A geometric approach to problems in physics, many of which cannot be solved by any other methods * Text is enriched with good examples and exercises at the end of every chapter * Fine for a course or seminar directed at grad and adv. undergrad students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics
An Introduction to Riemannian Geometry
An Introduction to Riemannian Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Riemannian Geometry write by Leonor Godinho. This book was released on 2014-07-26. An Introduction to Riemannian Geometry available in PDF, EPUB and Kindle. Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.
Sub-Riemannian Geometry
Sub-Riemannian Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Sub-Riemannian Geometry write by Ovidiu Calin. This book was released on 2009-04-20. Sub-Riemannian Geometry available in PDF, EPUB and Kindle. A comprehensive text and reference on sub-Riemannian and Heisenberg manifolds using a novel and robust variational approach.
On the Hypotheses Which Lie at the Bases of Geometry
On the Hypotheses Which Lie at the Bases of Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On the Hypotheses Which Lie at the Bases of Geometry write by Bernhard Riemann. This book was released on 2016-04-19. On the Hypotheses Which Lie at the Bases of Geometry available in PDF, EPUB and Kindle. This book presents William Clifford’s English translation of Bernhard Riemann’s classic text together with detailed mathematical, historical and philosophical commentary. The basic concepts and ideas, as well as their mathematical background, are provided, putting Riemann’s reasoning into the more general and systematic perspective achieved by later mathematicians and physicists (including Helmholtz, Ricci, Weyl, and Einstein) on the basis of his seminal ideas. Following a historical introduction that positions Riemann’s work in the context of his times, the history of the concept of space in philosophy, physics and mathematics is systematically presented. A subsequent chapter on the reception and influence of the text accompanies the reader from Riemann’s times to contemporary research. Not only mathematicians and historians of the mathematical sciences, but also readers from other disciplines or those with an interest in physics or philosophy will find this work both appealing and insightful.
Riemannian Geometry in an Orthogonal Frame
Riemannian Geometry in an Orthogonal Frame - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Riemannian Geometry in an Orthogonal Frame write by Elie Cartan. This book was released on 2001. Riemannian Geometry in an Orthogonal Frame available in PDF, EPUB and Kindle. Elie Cartan's book Geometry of Riemannian Manifolds (1928) was one of the best introductions to his methods. It was based on lectures given by the author at the Sorbonne in the academic year 1925-26. A modernized and extensively augmented edition appeared in 1946 (2nd printing, 1951, and 3rd printing, 1988). Cartan's lectures in 1926-27 were different -- he introduced exterior forms at the very beginning and used extensively orthonormal frames throughout to investigate the geometry of Riemannian manifolds. In this course he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. The lectures were translated into Russian in the book Riemannian Geometry in an Orthogonal Frame (1960). This book has many innovations, such as the notion of intrinsic normal differentiation and the Gaussian torsion of a submanifold in a Euclidean multidimensional space or in a space of constant curvature, an affine connection defined in a normal fiber bundle of a submanifold, etc. The only book of Elie Cartan that was not available in English, it has now been translated into English by Vladislav V Goldberg, the editor of the Russian edition.
