Share

Pseudo-Riemannian Geometry, [delta]-invariants and Applications

2011 Mathematics
Download Pseudo-Riemannian Geometry, [delta]-invariants and Applications PDF Online Free

Author :
Release : 2011
Genre : Mathematics
Kind : eBook
Book Rating : 630/5 ( reviews)

GET EBOOK


Book Synopsis Pseudo-Riemannian Geometry, [delta]-invariants and Applications by : Bang-yen Chen

Download or read book Pseudo-Riemannian Geometry, [delta]-invariants and Applications written by Bang-yen Chen. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Pseudo-riemannian Geometry, Delta-invariants And Applications

2011-03-23 Mathematics
Download Pseudo-riemannian Geometry, Delta-invariants And Applications PDF Online Free

Author :
Release : 2011-03-23
Genre : Mathematics
Kind : eBook
Book Rating : 489/5 ( reviews)

GET EBOOK


Book Synopsis Pseudo-riemannian Geometry, Delta-invariants And Applications by : Bang-yen Chen

Download or read book Pseudo-riemannian Geometry, Delta-invariants And Applications written by Bang-yen Chen. This book was released on 2011-03-23. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Laplacian on a Riemannian Manifold

1997-01-09 Mathematics
Download The Laplacian on a Riemannian Manifold PDF Online Free

Author :
Release : 1997-01-09
Genre : Mathematics
Kind : eBook
Book Rating : 312/5 ( reviews)

GET EBOOK


Book Synopsis The Laplacian on a Riemannian Manifold by : Steven Rosenberg

Download or read book The Laplacian on a Riemannian Manifold written by Steven Rosenberg. This book was released on 1997-01-09. Available in PDF, EPUB and Kindle. Book excerpt: This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.

Differential Geometry Of Warped Product Manifolds And Submanifolds

2017-05-29 Mathematics
Download Differential Geometry Of Warped Product Manifolds And Submanifolds PDF Online Free

Author :
Release : 2017-05-29
Genre : Mathematics
Kind : eBook
Book Rating : 945/5 ( reviews)

GET EBOOK


Book Synopsis Differential Geometry Of Warped Product Manifolds And Submanifolds by : Bang-yen Chen

Download or read book Differential Geometry Of Warped Product Manifolds And Submanifolds written by Bang-yen Chen. This book was released on 2017-05-29. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Eigenfunctions of the Laplacian on a Riemannian Manifold

2017-12-12 Mathematics
Download Eigenfunctions of the Laplacian on a Riemannian Manifold PDF Online Free

Author :
Release : 2017-12-12
Genre : Mathematics
Kind : eBook
Book Rating : 370/5 ( reviews)

GET EBOOK


Book Synopsis Eigenfunctions of the Laplacian on a Riemannian Manifold by : Steve Zelditch

Download or read book Eigenfunctions of the Laplacian on a Riemannian Manifold written by Steve Zelditch. This book was released on 2017-12-12. Available in PDF, EPUB and Kindle. Book excerpt: 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.

You may also like...