Differential Geometry Of Warped Product Manifolds And Submanifolds
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A01=Bang-yen Chen
Affine Space
Author_Bang-yen Chen
Black Hole
Category=PBMP
CR-Submanifold
CR-Warped Product
Delta-Invariant
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Kaehler Manifold
Lagrangian Submanifold
Nearly Kaehler Manifold
Para-Kaehler Manifold
Pseudo-Riemannian Manifold
Robertson-Walker Spacetime
RobertsonAcAEURA"Walker Spacetime
Robertson–Walker Spacetime
Sasakian Manifold
Semi-Riemannian Manifold
Slant Submanifolds
Spacetime
Submanifold
Warped Product Manifold
Warped Product Submanifold
Product details
- ISBN 9789813208926
- Publication Date: 17 Jul 2017
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
