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Author : S. R. Sario
Publisher : Springer
ISBN 13 : 354037261X
Total Pages : 518 pages
Book Rating : 4.5/5 (43 download)
Download or read book Classification Theory of Riemannian Manifolds written by S. R. Sario and published by Springer. This book was released on 2006-11-15 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Leo Sario
Publisher : Springer Science & Business Media
ISBN 13 : 3642482694
Total Pages : 469 pages
Book Rating : 4.6/5 (424 download)
Download or read book Classification Theory of Riemann Surfaces written by Leo Sario and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of the present monograph is to systematically develop a classification theory of Riemann surfaces. Some first steps will also be taken toward a classification of Riemannian spaces. Four phases can be distinguished in the chronological background: the type problem; general classification; compactifications; and extension to higher dimensions. The type problem evolved in the following somewhat overlapping steps: the Riemann mapping theorem, the classical type problem, and the existence of Green's functions. The Riemann mapping theorem laid the foundation to classification theory: there are only two conformal equivalence classes of (noncompact) simply connected regions. Over half a century of efforts by leading mathematicians went into giving a rigorous proof of the theorem: RIEMANN, WEIERSTRASS, SCHWARZ, NEUMANN, POINCARE, HILBERT, WEYL, COURANT, OSGOOD, KOEBE, CARATHEODORY, MONTEL. The classical type problem was to determine whether a given simply connected covering surface of the plane is conformally equivalent to the plane or the disko The problem was in the center of interest in the thirties and early forties, with AHLFORS, KAKUTANI, KOBAYASHI, P. MYRBERG, NEVANLINNA, SPEISER, TEICHMÜLLER and others obtaining incisive specific results. The main problem of finding necessary and sufficient conditions remains, however, unsolved.
Author : John M. Lee
Publisher : Springer Science & Business Media
ISBN 13 : 0387227261
Total Pages : 232 pages
Book Rating : 4.3/5 (872 download)
Download or read book Riemannian Manifolds written by John M. Lee and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.
Author : S. R. Sario
Publisher :
ISBN 13 : 9783662162927
Total Pages : 524 pages
Book Rating : 4.1/5 (629 download)
Download or read book Classification Theory of Riemannian Manifolds written by S. R. Sario and published by . This book was released on 2014-01-15 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : F. Tricerri
Publisher : Cambridge University Press
ISBN 13 : 0521274893
Total Pages : 145 pages
Book Rating : 4.5/5 (212 download)
Download or read book Homogeneous Structures on Riemannian Manifolds written by F. Tricerri and published by Cambridge University Press. This book was released on 1983-06-23 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this book is the theorem of Ambrose and Singer, which gives for a connected, complete and simply connected Riemannian manifold a necessary and sufficient condition for it to be homogeneous. This is a local condition which has to be satisfied at all points, and in this way it is a generalization of E. Cartan's method for symmetric spaces. The main aim of the authors is to use this theorem and representation theory to give a classification of homogeneous Riemannian structures on a manifold. There are eight classes, and some of these are discussed in detail. Using the constructive proof of Ambrose and Singer many examples are discussed with special attention to the natural correspondence between the homogeneous structure and the groups acting transitively and effectively as isometrics on the manifold.
Author : Loring W. Tu
Publisher : Springer Science & Business Media
ISBN 13 : 1441974008
Total Pages : 426 pages
Book Rating : 4.4/5 (419 download)
Download or read book An Introduction to Manifolds written by Loring W. Tu and published by Springer Science & Business Media. This book was released on 2010-10-05 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
Author : Leonor Godinho
Publisher : Springer
ISBN 13 : 3319086669
Total Pages : 476 pages
Book Rating : 4.3/5 (19 download)
Download or read book An Introduction to Riemannian Geometry written by Leonor Godinho and published by Springer. This book was released on 2014-07-26 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : John M. Lee
Publisher : Springer
ISBN 13 : 3319917552
Total Pages : 447 pages
Book Rating : 4.3/5 (199 download)
Download or read book Introduction to Riemannian Manifolds written by John M. Lee and published by Springer. This book was released on 2019-01-02 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.
Author : I. Laine
Publisher : Springer
ISBN 13 : 354034859X
Total Pages : 469 pages
Book Rating : 4.5/5 (43 download)
Download or read book Complex Analysis. Joensuu 1978 written by I. Laine and published by Springer. This book was released on 2006-11-15 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Romanian Finnish Seminar on Complex Analysis
Author : M.F. Newman
Publisher : Springer
ISBN 13 : 3540355499
Total Pages : 243 pages
Book Rating : 4.5/5 (43 download)
Download or read book Topics in Algebra written by M.F. Newman and published by Springer. This book was released on 2007-01-05 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ulrich Koschorke
Publisher : Springer
ISBN 13 : 3540391878
Total Pages : 507 pages
Book Rating : 4.5/5 (43 download)
Download or read book Topology Symposium Siegen 1979 written by Ulrich Koschorke and published by Springer. This book was released on 2006-12-08 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : P. Hoffman
Publisher : Springer
ISBN 13 : 3540350098
Total Pages : 668 pages
Book Rating : 4.5/5 (43 download)
Download or read book Algebraic Topology. Waterloo 1978 written by P. Hoffman and published by Springer. This book was released on 2006-11-15 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : R. Martini
Publisher : Springer
ISBN 13 : 354038166X
Total Pages : 350 pages
Book Rating : 4.5/5 (43 download)
Download or read book Geometrical Approaches to Differential Equations written by R. Martini and published by Springer. This book was released on 2006-11-15 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jürgen Eichhorn
Publisher : Nova Publishers
ISBN 13 : 9781600215636
Total Pages : 664 pages
Book Rating : 4.2/5 (156 download)
Download or read book Global Analysis on Open Manifolds written by Jürgen Eichhorn and published by Nova Publishers. This book was released on 2007 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Global analysis is the analysis on manifolds. Since the middle of the sixties there exists a highly elaborated setting if the underlying manifold is compact, evidence of which can be found in index theory, spectral geometry, the theory of harmonic maps, many applications to mathematical physics on closed manifolds like gauge theory, Seiberg-Witten theory, etc. If the underlying manifold is open, i.e. non-compact and without boundary, then most of the foundations and of the great achievements fail. Elliptic operators are no longer Fredholm, the analytical and topological indexes are not defined, the spectrum of self-adjoint elliptic operators is no longer discrete, functional spaces strongly depend on the operators involved and the data from geometry, many embedding and module structure theorems do not hold, manifolds of maps are not defined, etc. It is the goal of this new book to provide serious foundations for global analysis on open manifolds, to discuss the difficulties and special features which come from the openness and to establish many results and applications on this basis.
Author : Paul Baird
Publisher : Oxford University Press
ISBN 13 : 9780198503620
Total Pages : 540 pages
Book Rating : 4.5/5 (36 download)
Download or read book Harmonic Morphisms Between Riemannian Manifolds written by Paul Baird and published by Oxford University Press. This book was released on 2003 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an account in book form of the theory of harmonic morphisms between Riemannian manifolds.
Author : T. Terziogammalu
Publisher : Springer Science & Business Media
ISBN 13 : 9400924569
Total Pages : 375 pages
Book Rating : 4.4/5 (9 download)
Download or read book Advances in the Theory of Fréchet Spaces written by T. Terziogammalu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Frechet spaces have been studied since the days of Banach. These spaces, their inductive limits and their duals played a prominent role in the development of the theory of locally convex spaces. Also they are natural tools in many areas of real and complex analysis. The pioneering work of Grothendieck in the fifties has been one of the important sources of inspiration for research in the theory of Frechet spaces. A structure theory of nuclear Frechet spaces emerged and some important questions posed by Grothendieck were settled in the seventies. In particular, subspaces and quotient spaces of stable nuclear power series spaces were completely characterized. In the last years it has become increasingly clear that the methods used in the structure theory of nuclear Frechet spaces actually provide new insight to linear problems in diverse branches of analysis and lead to solutions of some classical problems. The unifying theme at our Workshop was the recent developments in the theory of the projective limit functor. This is appropriate because of the important role this theory had in the recent research. The main results of the structure theory of nuclear Frechet spaces can be formulated and proved within the framework of this theory. A major area of application of the theory of the projective limit functor is to decide when a linear operator is surjective and, if it is, to determine whether it has a continuous right inverse.
Author : C. H. C. Little
Publisher : Springer
ISBN 13 : 354037020X
Total Pages : 224 pages
Book Rating : 4.5/5 (43 download)
Download or read book Combinatorial Mathematics V. written by C. H. C. Little and published by Springer. This book was released on 2006-11-15 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
