Riemannian Topology and Geometric Structures on 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 Riemannian Topology and Geometric Structures on Manifolds write by Krzysztof Galicki. This book was released on 2010-07-25. Riemannian Topology and Geometric Structures on Manifolds available in PDF, EPUB and Kindle. Riemannian Topology and Structures on Manifolds results from a similarly entitled conference held on the occasion of Charles P. Boyer’s 65th birthday. The various contributions to this volume discuss recent advances in the areas of positive sectional curvature, Kähler and Sasakian geometry, and their interrelation to mathematical physics, especially M and superstring theory. Focusing on these fundamental ideas, this collection presents review articles, original results, and open problems of interest.
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.
Metric Structures for Riemannian and Non-Riemannian Spaces
Metric Structures for Riemannian and Non-Riemannian Spaces - 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 Metric Structures for Riemannian and Non-Riemannian Spaces write by Mikhail Gromov. This book was released on 2007-06-25. Metric Structures for Riemannian and Non-Riemannian Spaces available in PDF, EPUB and Kindle. This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.
Geometry and Topology of Manifolds: Surfaces and Beyond
Geometry and Topology of Manifolds: Surfaces and Beyond - 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 Geometry and Topology of Manifolds: Surfaces and Beyond write by Vicente Muñoz. This book was released on 2020-10-21. Geometry and Topology of Manifolds: Surfaces and Beyond available in PDF, EPUB and Kindle. This book represents a novel approach to differential topology. Its main focus is to give a comprehensive introduction to the classification of manifolds, with special attention paid to the case of surfaces, for which the book provides a complete classification from many points of view: topological, smooth, constant curvature, complex, and conformal. Each chapter briefly revisits basic results usually known to graduate students from an alternative perspective, focusing on surfaces. We provide full proofs of some remarkable results that sometimes are missed in basic courses (e.g., the construction of triangulations on surfaces, the classification of surfaces, the Gauss-Bonnet theorem, the degree-genus formula for complex plane curves, the existence of constant curvature metrics on conformal surfaces), and we give hints to questions about higher dimensional manifolds. Many examples and remarks are scattered through the book. Each chapter ends with an exhaustive collection of problems and a list of topics for further study. The book is primarily addressed to graduate students who did take standard introductory courses on algebraic topology, differential and Riemannian geometry, or algebraic geometry, but have not seen their deep interconnections, which permeate a modern approach to geometry and topology of manifolds.
Lectures on the Geometry of Manifolds
Lectures on the Geometry of 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 Lectures on the Geometry of Manifolds write by Liviu I. Nicolaescu. This book was released on 2007. Lectures on the Geometry of Manifolds available in PDF, EPUB and Kindle. The goal of this book is to introduce the reader to some of the most frequently used techniques in modern global geometry. Suited to the beginning graduate student willing to specialize in this very challenging field, the necessary prerequisite is a good knowledge of several variables calculus, linear algebra and point-set topology.The book's guiding philosophy is, in the words of Newton, that ?in learning the sciences examples are of more use than precepts?. We support all the new concepts by examples and, whenever possible, we tried to present several facets of the same issue.While we present most of the local aspects of classical differential geometry, the book has a ?global and analytical bias?. We develop many algebraic-topological techniques in the special context of smooth manifolds such as Poincar duality, Thom isomorphism, intersection theory, characteristic classes and the Gauss-;Bonnet theorem.We devoted quite a substantial part of the book to describing the analytic techniques which have played an increasingly important role during the past decades. Thus, the last part of the book discusses elliptic equations, including elliptic Lpand Hlder estimates, Fredholm theory, spectral theory, Hodge theory, and applications of these. The last chapter is an in-depth investigation of a very special, but fundamental class of elliptic operators, namely, the Dirac type operators.The second edition has many new examples and exercises, and an entirely new chapter on classical integral geometry where we describe some mathematical gems which, undeservedly, seem to have disappeared from the contemporary mathematical limelight.
