Pseudo Riemannian Geometry Delta Invariants And Applications
Download Pseudo Riemannian Geometry Delta Invariants And Applications full books in PDF, epub, and Kindle. Read online free Pseudo Riemannian Geometry Delta Invariants And Applications ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Author | : Bang-yen Chen |
Publisher | : World Scientific |
Total Pages | : 510 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 9814329630 |
Download Pseudo-Riemannian Geometry, [delta]-invariants and Applications Book in PDF, Epub and Kindle
The first part of this book provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian manifolds and their non-degenerate submanifolds, only assuming from the reader some basic knowledge about manifold theory. A number of recent results on pseudo-Riemannian submanifolds are also included.The second part of this book is on ë-invariants, which was introduced in the early 1990s by the author. The famous Nash embedding theorem published in 1956 was aimed for, in the hope that if Riemannian manifolds could be regarded as Riemannian submanifolds, this would then yield the opportunity to use extrinsic help. However, this hope had not been materialized as pointed out by M Gromov in his 1985 article published in Asterisque. The main reason for this is the lack of control of the extrinsic invariants of the submanifolds by known intrinsic invariants. In order to overcome such difficulties, as well as to provide answers for an open question on minimal immersions, the author introduced in the early 1990s new types of Riemannian invariants, known as ë-invariants, which are very different in nature from the classical Ricci and scalar curvatures. At the same time he was able to establish general optimal relations between ë-invariants and the main extrinsic invariants. Since then many new results concerning these ë-invariants have been obtained by many geometers. The second part of this book is to provide an extensive and comprehensive survey over this very active field of research done during the last two decades.
Author | : Bang-yen Chen |
Publisher | : World Scientific |
Total Pages | : 510 |
Release | : 2011-03-23 |
Genre | : Mathematics |
ISBN | : 9814462489 |
Download Pseudo-riemannian Geometry, Delta-invariants And Applications Book in PDF, Epub and Kindle
The first part of this book provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian manifolds and their non-degenerate submanifolds, only assuming from the reader some basic knowledge about manifold theory. A number of recent results on pseudo-Riemannian submanifolds are also included.The second part of this book is on δ-invariants, which was introduced in the early 1990s by the author. The famous Nash embedding theorem published in 1956 was aimed for, in the hope that if Riemannian manifolds could be regarded as Riemannian submanifolds, this would then yield the opportunity to use extrinsic help. However, this hope had not been materialized as pointed out by M Gromov in his 1985 article published in Asterisque. The main reason for this is the lack of control of the extrinsic invariants of the submanifolds by known intrinsic invariants. In order to overcome such difficulties, as well as to provide answers for an open question on minimal immersions, the author introduced in the early 1990s new types of Riemannian invariants, known as δ-invariants, which are very different in nature from the classical Ricci and scalar curvatures. At the same time he was able to establish general optimal relations between δ-invariants and the main extrinsic invariants. Since then many new results concerning these δ-invariants have been obtained by many geometers. The second part of this book is to provide an extensive and comprehensive survey over this very active field of research done during the last two decades.
Author | : Steven Rosenberg |
Publisher | : Cambridge University Press |
Total Pages | : 190 |
Release | : 1997-01-09 |
Genre | : Mathematics |
ISBN | : 9780521468312 |
Download The Laplacian on a Riemannian Manifold Book in PDF, Epub and Kindle
This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.
Author | : Steve Zelditch |
Publisher | : American Mathematical Soc. |
Total Pages | : 410 |
Release | : 2017-12-12 |
Genre | : Mathematics |
ISBN | : 1470410370 |
Download Eigenfunctions of the Laplacian on a Riemannian Manifold Book in PDF, Epub and Kindle
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.
Author | : Barrett O'Neill |
Publisher | : Academic Press |
Total Pages | : 483 |
Release | : 1983-07-29 |
Genre | : Mathematics |
ISBN | : 0080570577 |
Download Semi-Riemannian Geometry With Applications to Relativity Book in PDF, Epub and Kindle
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 | : Danny Calegari |
Publisher | : Oxford University Press on Demand |
Total Pages | : 378 |
Release | : 2007-05-17 |
Genre | : Mathematics |
ISBN | : 0198570082 |
Download Foliations and the Geometry of 3-Manifolds Book in PDF, Epub and Kindle
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
Author | : Aurel Bejancu |
Publisher | : Springer Science & Business Media |
Total Pages | : 202 |
Release | : 1986-07-31 |
Genre | : Mathematics |
ISBN | : 9789027721945 |
Download Geometry of CR-Submanifolds Book in PDF, Epub and Kindle
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can us;; Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Author | : Bang-yen Chen |
Publisher | : World Scientific |
Total Pages | : 517 |
Release | : 2017-05-29 |
Genre | : Mathematics |
ISBN | : 9813208945 |
Download Differential Geometry Of Warped Product Manifolds And Submanifolds Book in PDF, Epub and Kindle
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 | : John Roe |
Publisher | : Longman Scientific and Technical |
Total Pages | : 208 |
Release | : 1988 |
Genre | : Mathematics |
ISBN | : |
Download Elliptic Operators, Topology, and Asymptotic Methods Book in PDF, Epub and Kindle
Author | : |
Publisher | : |
Total Pages | : 770 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : |
Download Mathematical Reviews Book in PDF, Epub and Kindle