Tensors And Riemannian Geometry
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| Author | : Nail H. Ibragimov |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 198 |
| Release | : 2015-08-31 |
| Genre | : Mathematics |
| ISBN | : 3110379503 |
This book is based on the experience of teaching the subject by the author in Russia, France, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics on tensors, Riemannian geometry and geometric approach to partial differential equations. Application of approximate transformation groups to the equations of general relativity in the de Sitter space simplifies the subject significantly.
| Author | : K.K. Dube |
| Publisher | : I. K. International Pvt Ltd |
| Total Pages | : 377 |
| Release | : 2013-12-30 |
| Genre | : Mathematics |
| ISBN | : 9380026587 |
The purpose of this book is to give a simple, lucid, rigorous and comprehensive account of fundamental notions of Differential Geometry and Tensors. The book is self-contained and divided in two parts. Section A deals with Differential Geometry and Section B is devoted to the study of Tensors. Section A deals with: " Theory of curves, envelopes and developables. " Curves on surfaces and fundamental magnitudes, curvature of surfaces and lines of curvature. " Fundamental equations of surface theory. " Geodesics. Section B deals with: " Tensor algebra. " Tensor calculus. " Christoffel symbols and their properties. " Riemann symbols and Einstein space, and their properties. " Physical components of contravariant and covariant vectors. " Geodesics and Parallelism of vectors. " Differentiable manifolds, charts, atlases.
| Author | : Charles Ernest Weatherburn |
| Publisher | : CUP Archive |
| Total Pages | : 214 |
| Release | : 1938 |
| Genre | : Calculus of tensors |
| ISBN | : |
| Author | : Bernhard Riemann |
| Publisher | : Birkhäuser |
| Total Pages | : 181 |
| Release | : 2016-04-19 |
| Genre | : Mathematics |
| ISBN | : 3319260421 |
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.
| Author | : Tracy Y. Thomas |
| Publisher | : Elsevier |
| Total Pages | : 128 |
| Release | : 2016-06-03 |
| Genre | : Mathematics |
| ISBN | : 1483263711 |
Concepts from Tensor Analysis and Differential Geometry discusses coordinate manifolds, scalars, vectors, and tensors. The book explains some interesting formal properties of a skew-symmetric tensor and the curl of a vector in a coordinate manifold of three dimensions. It also explains Riemann spaces, affinely connected spaces, normal coordinates, and the general theory of extension. The book explores differential invariants, transformation groups, Euclidean metric space, and the Frenet formulae. The text describes curves in space, surfaces in space, mixed surfaces, space tensors, including the formulae of Gaus and Weingarten. It presents the equations of two scalars K and Q which can be defined over a regular surface S in a three dimensional Riemannian space R. In the equation, the scalar K, which is an intrinsic differential invariant of the surface S, is known as the total or Gaussian curvature and the scalar U is the mean curvature of the surface. The book also tackles families of parallel surfaces, developable surfaces, asymptotic lines, and orthogonal ennuples. The text is intended for a one-semester course for graduate students of pure mathematics, of applied mathematics covering subjects such as the theory of relativity, fluid mechanics, elasticity, and plasticity theory.
| Author | : David Lovelock |
| Publisher | : Courier Corporation |
| Total Pages | : 402 |
| Release | : 2012-04-20 |
| Genre | : Mathematics |
| ISBN | : 048613198X |
Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.
| Author | : Ralph Abraham |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 666 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461210291 |
The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid me chanics, electromagnetism, plasma dynamics and control thcory arc given in Chapter 8, using both invariant and index notation. The current edition of the book does not deal with Riemannian geometry in much detail, and it does not treat Lie groups, principal bundles, or Morse theory. Some of this is planned for a subsequent edition. Meanwhile, the authors will make available to interested readers supplementary chapters on Lie Groups and Differential Topology and invite comments on the book's contents and development. Throughout the text supplementary topics are given, marked with the symbols ~ and {l:;J. This device enables the reader to skip various topics without disturbing the main flow of the text. Some of these provide additional background material intended for completeness, to minimize the necessity of consulting too many outside references. We treat finite and infinite-dimensional manifolds simultaneously. This is partly for efficiency of exposition. Without advanced applications, using manifolds of mappings, the study of infinite-dimensional manifolds can be hard to motivate.
| Author | : Barrett O'Neill |
| Publisher | : Academic Press |
| Total Pages | : 483 |
| Release | : 1983-07-29 |
| Genre | : Mathematics |
| ISBN | : 0080570577 |
This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest.
| Author | : Paul Renteln |
| Publisher | : Cambridge University Press |
| Total Pages | : 343 |
| Release | : 2014 |
| Genre | : Mathematics |
| ISBN | : 1107042194 |
Comprehensive treatment of the essentials of modern differential geometry and topology for graduate students in mathematics and the physical sciences.
| Author | : Hung Nguyen-Schäfer |
| Publisher | : Springer |
| Total Pages | : 389 |
| Release | : 2016-08-16 |
| Genre | : Technology & Engineering |
| ISBN | : 3662484978 |
This book presents tensors and differential geometry in a comprehensive and approachable manner, providing a bridge from the place where physics and engineering mathematics end, and the place where tensor analysis begins. Among the topics examined are tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. The book includes numerous examples with solutions and concrete calculations, which guide readers through these complex topics step by step. Mindful of the practical needs of engineers and physicists, book favors simplicity over a more rigorous, formal approach. The book shows readers how to work with tensors and differential geometry and how to apply them to modeling the physical and engineering world. The authors provide chapter-length treatment of topics at the intersection of advanced mathematics, and physics and engineering: • General Basis and Bra-Ket Notation • Tensor Analysis • Elementary Differential Geometry • Differential Forms • Applications of Tensors and Differential Geometry • Tensors and Bra-Ket Notation in Quantum Mechanics The text reviews methods and applications in computational fluid dynamics; continuum mechanics; electrodynamics in special relativity; cosmology in the Minkowski four-dimensional space time; and relativistic and non-relativistic quantum mechanics. Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers benefits research scientists and practicing engineers in a variety of fields, who use tensor analysis and differential geometry in the context of applied physics, and electrical and mechanical engineering. It will also interest graduate students in applied physics and engineering.
