Differential Geometry Of Warped Product Manifolds And Submanifolds is popular PDF and ePub book, written by Bang-yen Chen in 2017-05-29, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Differential Geometry Of Warped Product Manifolds And Submanifolds can be Read Online from any device for your convenience.
Differential Geometry Of Warped Product Manifolds And Submanifolds Book PDF Summary
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.
Detail Book of Differential Geometry Of Warped Product Manifolds And Submanifolds PDF
- Author : Bang-yen Chen
- Release : 29 May 2017
- Publisher : World Scientific
- ISBN : 9789813208940
- Genre : Mathematics
- Total Page : 517 pages
- Language : English
- PDF File Size : 11,6 Mb
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