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| Author | : International Council for Traditional Music. Study Group Music and Minorities. Meeting |
| Publisher | : Cambridge Scholars Press |
| Total Pages | : 372 |
| Release | : 2004 |
| Genre | : Church music |
| ISBN | : 1904303374 |
This is a study of manifold identities focusing on music and musicology.
| Author | : Vladimir Rovenski |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 296 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461242703 |
This monograph is based on the author's results on the Riemannian ge ometry of foliations with nonnegative mixed curvature and on the geometry of sub manifolds with generators (rulings) in a Riemannian space of nonnegative curvature. The main idea is that such foliated (sub) manifolds can be decom posed when the dimension of the leaves (generators) is large. The methods of investigation are mostly synthetic. The work is divided into two parts, consisting of seven chapters and three appendices. Appendix A was written jointly with V. Toponogov. Part 1 is devoted to the Riemannian geometry of foliations. In the first few sections of Chapter I we give a survey of the basic results on foliated smooth manifolds (Sections 1.1-1.3), and finish in Section 1.4 with a discussion of the key problem of this work: the role of Riemannian curvature in the study of foliations on manifolds and submanifolds.
| Author | : John M. Lee |
| Publisher | : Springer |
| Total Pages | : 437 |
| Release | : 2019-01-02 |
| Genre | : Mathematics |
| ISBN | : 3319917552 |
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 | : Eduardo Cattani |
| Publisher | : Princeton University Press |
| Total Pages | : 608 |
| Release | : 2014-07-21 |
| Genre | : Mathematics |
| ISBN | : 1400851475 |
This book provides a comprehensive and up-to-date introduction to Hodge theory—one of the central and most vibrant areas of contemporary mathematics—from leading specialists on the subject. The topics range from the basic topology of algebraic varieties to the study of variations of mixed Hodge structure and the Hodge theory of maps. Of particular interest is the study of algebraic cycles, including the Hodge and Bloch-Beilinson Conjectures. Based on lectures delivered at the 2010 Summer School on Hodge Theory at the ICTP in Trieste, Italy, the book is intended for a broad group of students and researchers. The exposition is as accessible as possible and doesn't require a deep background. At the same time, the book presents some topics at the forefront of current research. The book is divided between introductory and advanced lectures. The introductory lectures address Kähler manifolds, variations of Hodge structure, mixed Hodge structures, the Hodge theory of maps, period domains and period mappings, algebraic cycles (up to and including the Bloch-Beilinson conjecture) and Chow groups, sheaf cohomology, and a new treatment of Grothendieck’s algebraic de Rham theorem. The advanced lectures address a Hodge-theoretic perspective on Shimura varieties, the spread philosophy in the study of algebraic cycles, absolute Hodge classes (including a new, self-contained proof of Deligne’s theorem on absolute Hodge cycles), and variation of mixed Hodge structures. The contributors include Patrick Brosnan, James Carlson, Eduardo Cattani, François Charles, Mark Andrea de Cataldo, Fouad El Zein, Mark L. Green, Phillip A. Griffiths, Matt Kerr, Lê Dũng Tráng, Luca Migliorini, Jacob P. Murre, Christian Schnell, and Loring W. Tu.
| Author | : Daniel W. Stroock |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 290 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 0821838393 |
Hoping to make the text more accessible to readers not schooled in the probabalistic tradition, Stroock (affiliation unspecified) emphasizes the geometric over the stochastic analysis of differential manifolds. Chapters deconstruct Brownian paths, diffusions in Euclidean space, intrinsic and extrinsic Riemannian geometry, Bocher's identity, and the bundle of orthonormal frames. The volume humbly concludes with an "admission of defeat" in regard to recovering the Li-Yau basic differential inequality. Annotation copyrighted by Book News, Inc., Portland, OR.
| Author | : Bang-yen Chen |
| Publisher | : World Scientific |
| Total Pages | : 517 |
| Release | : 2017-05-29 |
| Genre | : Mathematics |
| ISBN | : 9813208945 |
A warped product manifold is a Riemannian or pseudo-Riemannian manifold whose metric tensor can be decomposed into a Cartesian product of the y geometry and the x geometry — except that the x-part is warped, that is, it is rescaled by a scalar function of the other coordinates y. The notion of warped product manifolds plays very important roles not only in geometry but also in mathematical physics, especially in general relativity. In fact, many basic solutions of the Einstein field equations, including the Schwarzschild solution and the Robertson-Walker models, are warped product manifolds.The first part of this volume provides a self-contained and accessible introduction to the important subject of pseudo-Riemannian manifolds and submanifolds. The second part presents a detailed and up-to-date account on important results of warped product manifolds, including several important spacetimes such as Robertson-Walker's and Schwarzschild's.The famous John Nash's embedding theorem published in 1956 implies that every warped product manifold can be realized as a warped product submanifold in a suitable Euclidean space. The study of warped product submanifolds in various important ambient spaces from an extrinsic point of view was initiated by the author around the beginning of this century.The last part of this volume contains an extensive and comprehensive survey of numerous important results on the geometry of warped product submanifolds done during this century by many geometers.
| Author | : Uday Chand De |
| Publisher | : Alpha Science International, Limited |
| Total Pages | : 320 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : |
Differential Geometry of Manifolds discusses the theory of differentiable and Riemannian manifolds to help students understand the basic structures and consequent developments. Since the tangent vector plays a crucial role in the study of differentiable manifolds, this idea has been thoroughly discussed. In the theory of Riemannian geometry some new proofs have been included to enable the reader understand the subject in a comprehensive and systematic manner. This book will also benefit the postgraduate students as well as researchers working in the field of differential geometry and its applications to general relativity and cosmology.
| Author | : Lev Sabinin |
| Publisher | : CRC Press |
| Total Pages | : 558 |
| Release | : 2006-01-13 |
| Genre | : Mathematics |
| ISBN | : 9780824726690 |
With contributions derived from presentations at an international conference, Non-Associative Algebra and Its Applications explores a wide range of topics focusing on Lie algebras, nonassociative rings and algebras, quasigroups, loops, and related systems as well as applications of nonassociative algebra to geometry, physics, and natural sciences. This book covers material such as Jordan superalgebras, nonassociative deformations, nonassociative generalization of Hopf algebras, the structure of free algebras, derivations of Lie algebras, and the identities of Albert algebra. It also includes applications of smooth quasigroups and loops to differential geometry and relativity.
| Author | : Parag Khanna |
| Publisher | : Simon and Schuster |
| Total Pages | : 352 |
| Release | : 2021-10-12 |
| Genre | : Business & Economics |
| ISBN | : 1982168978 |
"In the 60,000 years since people began colonizing the continents, a continuous feature of human civilization has been mobility. History is replete with seismic global events-pandemics and plagues, wars and genocides. Each time, after a great catastrophe, our innate impulse toward physical security compels us to move. The map of humanity isn't settled-not now, not ever. The filled-with-crises 21st century promises to contain the most dangerous and extensive experiment humanity has ever run on itself: As climates change, pandemics arrive, and economies rise and fall, which places will people leave and where will they resettle? Which countries will accept or reject them? How will the billions alive today, and the billions coming, paint the next map of human geography? Until now, the study of human geography and migration has been like a weather forecast. Move delivers an authoritative look at the "climate" of migration, the deep trends that will shape the grand economic and security scenarios of the future. For readers, it will be a chance to identify their location on humanity's next map"--
| Author | : Steve Zelditch |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 410 |
| Release | : 2017-12-12 |
| Genre | : Mathematics |
| ISBN | : 1470410370 |
Eigenfunctions of the Laplacian of a Riemannian manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates. This book is an introduction to both the local and global analysis of eigenfunctions. The local analysis of eigenfunctions pertains to the behavior of the eigenfunctions on wavelength scale balls. After re-scaling to a unit ball, the eigenfunctions resemble almost-harmonic functions. Global analysis refers to the use of wave equation methods to relate properties of eigenfunctions to properties of the geodesic flow. The emphasis is on the global methods and the use of Fourier integral operator methods to analyze norms and nodal sets of eigenfunctions. A somewhat unusual topic is the analytic continuation of eigenfunctions to Grauert tubes in the real analytic case, and the study of nodal sets in the complex domain. The book, which grew out of lectures given by the author at a CBMS conference in 2011, provides complete proofs of some model results, but more often it gives informal and intuitive explanations of proofs of fairly recent results. It conveys inter-related themes and results and offers an up-to-date comprehensive treatment of this important active area of research.
