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E Cartan Lecons Sur La Geometrie Des Espaces De Riemann
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Book Synopsis Riemannian Geometry During the Second Half of the Twentieth Century by : Marcel Berger
Download or read book Riemannian Geometry During the Second Half of the Twentieth Century written by Marcel Berger and published by American Mathematical Soc.. This book was released on 2000 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: During its first hundred years, Riemannian geometry enjoyed steady, but undistinguished growth as a field of mathematics. In the last fifty years of the twentieth century, however, it has exploded with activity. Berger marks the start of this period with Rauch's pioneering paper of 1951, which contains the first real pinching theorem and an amazing leap in the depth of the connection between geometry and topology. Since then, the field has become so rich that it is almost impossible for the uninitiated to find their way through it. Textbooks on the subject invariably must choose a particular approach, thus narrowing the path. In this book, Berger provides a remarkable survey of the main developments in Riemannian geometry in the second half of the last fifty years. One of the most powerful features of Riemannian manifolds is that they have invariants of (at least) three different kinds. There are the geometric invariants: topology, the metric, various notions of curvature, and relationships among these. There are analytic invariants: eigenvalues of the Laplacian, wave equations, Schrödinger equations. There are the invariants that come from Hamiltonian mechanics: geodesic flow, ergodic properties, periodic geodesics. Finally, there are important results relating different types of invariants. To keep the size of this survey manageable, Berger focuses on five areas of Riemannian geometry: Curvature and topology; the construction of and the classification of space forms; distinguished metrics, especially Einstein metrics; eigenvalues and eigenfunctions of the Laplacian; the study of periodic geodesics and the geodesic flow. Other topics are treated in less detail in a separate section. While Berger's survey is not intended for the complete beginner (one should already be familiar with notions of curvature and geodesics), he provides a detailed map to the major developments of Riemannian geometry from 1950 to 1999. Important threads are highlighted, with brief descriptions of the results that make up that thread. This supremely scholarly account is remarkable for its careful citations and voluminous bibliography. If you wish to learn about the results that have defined Riemannian geometry in the last half century, start with this book.
Book Synopsis Riemannian Geometry in an Orthogonal Frame by : Elie Cartan
Download or read book Riemannian Geometry in an Orthogonal Frame written by Elie Cartan and published by World Scientific. This book was released on 2001 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fundamentals of Differential Geometry by : Serge Lang
Download or read book Fundamentals of Differential Geometry written by Serge Lang and published by Springer Science & Business Media. This book was released on 2001-09-21 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER
Book Synopsis Riemannian Geometry by : Luther Pfahler Eisenhart
Download or read book Riemannian Geometry written by Luther Pfahler Eisenhart and published by Princeton University Press. This book was released on 1997-11-02 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: In his classic work of geometry, Euclid focused on the properties of flat surfaces. The study of curved surfaces, or non-Euclidean geometry, flowered in the late 19th century, thanks to mathematicians such as Riemann. In this book, Luther Eisenhart succinctly surveys the key concepts of Riemannian geometry, addressing mathematicians and theoretical physicists alike.
Book Synopsis Spectral Theory of Random Matrices by : Vyacheslav L. Girko
Download or read book Spectral Theory of Random Matrices written by Vyacheslav L. Girko and published by Academic Press. This book was released on 2016-08-23 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral Theory of Random Matrices
Book Synopsis Encyclopaedia of Mathematics by : M. Hazewinkel
Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-12-01 with total page 967 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer. This book was released on 2013-12-20 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Linear and Nonlinear Functional Analysis with Applications by : Philippe G. Ciarlet
Download or read book Linear and Nonlinear Functional Analysis with Applications written by Philippe G. Ciarlet and published by SIAM. This book was released on 2013-10-10 with total page 847 pages. Available in PDF, EPUB and Kindle. Book excerpt: This single-volume textbook covers the fundamentals of linear and nonlinear functional analysis, illustrating most of the basic theorems with numerous applications to linear and nonlinear partial differential equations and to selected topics from numerical analysis and optimization theory. This book has pedagogical appeal because it features self-contained and complete proofs of most of the theorems, some of which are not always easy to locate in the literature or are difficult to reconstitute. It also offers 401 problems and 52 figures, plus historical notes and many original references that provide an idea of the genesis of the important results, and it covers most of the core topics from functional analysis.
Book Synopsis Geometry in Condensed Matter Physics by : J. F. Sadoc
Download or read book Geometry in Condensed Matter Physics written by J. F. Sadoc and published by World Scientific. This book was released on 1990 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of geometry has become an important ingredient in condensed matter physics. It appears not only to describe, but also to explain structures and their properties. There are two aspects to using geometry: the visual and intuitive understanding, which fosters an immediate grasp of the objects one studies, and the abstract tendency so well developed in the Riemannian manifold theory. Both aspects contribute to the same understanding when they are applied to the main problems occurring in condensed matter sciences. Sophisticated structures found in nature appear naturally as the result of simple constraints which are presented in geometrical terms. Blue phases, amorphous and glassy materials, Frank and Kasper Metals, quasi-crystals are approached in their complexity, using the simple principles of geometry. The relation between biology and liquid crystal sciences, the physics of membranes is a fundamental aspect presented in this book.
Book Synopsis Differential Geometry with Applications to Mechanics and Physics by : Yves Talpaert
Download or read book Differential Geometry with Applications to Mechanics and Physics written by Yves Talpaert and published by CRC Press. This book was released on 2000-09-12 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to differential geometry with applications to mechanics and physics. It covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms; exterior differential
Book Synopsis Mechanics in Differential Geometry by : Yves Talpaert
Download or read book Mechanics in Differential Geometry written by Yves Talpaert and published by Walter de Gruyter. This book was released on 2012-03-20 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Journal of the London Mathematical Society by : London Mathematical Society
Download or read book Journal of the London Mathematical Society written by London Mathematical Society and published by . This book was released on 1928 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Mathematical Heritage of Henri Poincaré by : Felix E. Browder
Download or read book The Mathematical Heritage of Henri Poincaré written by Felix E. Browder and published by American Mathematical Soc.. This book was released on 1983 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: On April 7-10, 1980, the American Mathematical Society sponsored a Symposium on the Mathematical Heritage of Henri Poincari, held at Indiana University, Bloomington, Indiana. This title presents the written versions this Symposium. It contains two papers by invited speakers who were not able to attend, S S Chern and L Nirenberg.
Book Synopsis Differential Geometry by : I. M. James
Download or read book Differential Geometry written by I. M. James and published by Elsevier. This book was released on 2014-05-16 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematical Works of J. H. C. Whitehead, Volume 1: Differential Geometry contains all of Whitehead's published work on differential geometry, along with some papers on algebras. Most of these were written in the period 1929-1937, but a few later articles are included. The book begins with a list of Whitehead's works, in chronological order of writing as well as a biographical note by M. H. A. Newman and Barbara Whitehead, and a mathematical appreciation by John Milnor. This is followed by separate chapters on topics such as linear connections; a method of obtaining normal representations for a projective connection; representation of projective spaces; convex regions in the geometry of paths; locally homogeneous spaces in differential geometry; and the decomposition of an infinitesimal group. Also included are chapters on locally homogeneous spaces in differential geometry; Maurer's equations; linear associative algebras; an expression of Hopf's invariant as an integral; and normalizators of transformation groups.
Book Synopsis Semisimple Groups and Riemannian Symmetric Spaces by : Armand Borel
Download or read book Semisimple Groups and Riemannian Symmetric Spaces written by Armand Borel and published by Springer. This book was released on 1998-12-15 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quantum Field Theory and Critical Phenomena by : Jean Zinn-Justin
Download or read book Quantum Field Theory and Critical Phenomena written by Jean Zinn-Justin and published by Oxford University Press. This book was released on 2021-04-15 with total page 1100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduced as a quantum extension of Maxwell's classical theory, quantum electrodynamics has been the first example of a Quantum Field Theory (QFT). Eventually, QFT has become the framework for the discussion of all fundamental interactions at the microscopic scale except, possibly, gravity. More surprisingly, it has also provided a framework for the understanding of second order phase transitions in statistical mechanics. As this work illustrates, QFT is the natural framework for the discussion of most systems involving an infinite number of degrees of freedom with local couplings. These systems range from cold Bose gases at the condensation temperature (about ten nanokelvin) to conventional phase transitions (from a few degrees to several hundred) and high energy particle physics up to a TeV, altogether more than twenty orders of magnitude in the energy scale. Therefore, this text sets out to present a work in which the strong formal relations between particle physics and the theory of critical phenomena are systematically emphasized. This option explains some of the choices made in the presentation. A formulation in terms of field integrals has been adopted to study the properties of QFT. The language of partition and correlation functions has been used throughout, even in applications of QFT to particle physics. Renormalization and renormalization group properties are systematically discussed. The notion of effective field theory and the emergence of renormalisable theories are described. The consequences for fine tuning and triviality issue are emphasized. This fifth edition has been updated and fully revised, e.g. in particle physics with progress in neutrino physics and the discovery of the Higgs boson. The presentation has been made more homogeneous througout the volume, and emphasis has been put on the notion of effective field theory and discussion of the emergence of renormalisable theories.
Book Synopsis Mechanics of Generalized Continua by : E. Kröner
Download or read book Mechanics of Generalized Continua written by E. Kröner and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 5 The symposium was held in Freudenstadt from 28\h to 31 \ ofAugust st nd 1967 and in Stuttgart from 1 to 2 of September 1967. The proposal to hold this symposium originated with the German Society of Applied Mathematics and Mechanics (GAMM) late in 1964 and was examined by a committee of IUTAM especially appointed for this purpose. The basis of this examination was a report in which the present situation in the field and the possible aims of the symposium were surveyed. Briefly, the aims of the symposium were stated to be 1. the unification of the various approaches developed in recent years with the aim of penetrating into the microscopic world of matter by means of continuum theories; 2. the bridging of the gap between microscopic (or atomic) research on mechanics on one hand, and the phenomenological (or continuum mechanical) approach on the other hand; 3. the physical interpretation and the relation to actual material behaviour of the quantities and laws introduced into the new theories, together with applications; 4. the further development of the theories, where necessary, and the clarification of open questions; 5. a stocktaking of present achievements and the prognosis for future developments. The committee agreed unanimously that the topic of the symposium represented an important phase of current developments in continuum mechanics, from the purely theoretical point of view as well as in connection with possible applications to actual materials.
