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Bang-yen Chen
Differential Geometry Of Warped Product Manifolds And Submanifolds
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2364822Differential Geometry Of Warped Product Manifolds And Submanifoldshttps://www.gandhi.com.mx/differential-geometry-of-warped-product-manifolds-and-submanifolds-9789813208940/phttps://gandhi.vtexassets.com/arquivos/ids/3599739/d8d2c509-eb42-4b98-8826-fea11c1b5617.jpg?v=63838560762590000023262584MXNWorld Scientific Publishing CompanyInStock/Ebooks/<p>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-Walkers and Schwarzschilds.The famous John Nashs 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.</p>...2301284Differential Geometry Of Warped Product Manifolds And Submanifolds23262584https://www.gandhi.com.mx/differential-geometry-of-warped-product-manifolds-and-submanifolds-9789813208940/phttps://gandhi.vtexassets.com/arquivos/ids/3599739/d8d2c509-eb42-4b98-8826-fea11c1b5617.jpg?v=638385607625900000InStockMXN99999DIEbook20179789813208940_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_<p>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-Walkers and Schwarzschilds.The famous John Nashs 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.</p>(*_*)9789813208940_<p>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-Walkers and Schwarzschilds.The famous John Nashs 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.</p>...9789813208940_World Scientific Publishing Companylibro_electonico_19b28645-c569-3c8f-bad2-aeb9ef245955_9789813208940;9789813208940_9789813208940Bang-yen ChenInglésMéxicohttps://getbook.kobo.com/koboid-prod-public/worldscientific-epub-d2f409bd-1d2c-4867-9272-aeb38be51ce7.epub2017-05-29T00:00:00+00:00World Scientific Publishing Company