Differential geometry of warped product manifolds and submanifolds:
"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...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Publishing Co. Pte Ltd.
c2017
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| Schlagworte: | |
| Online-Zugang: | FHN01 Volltext |
| Zusammenfassung: | "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.."--Publisher's website |
| Beschreibung: | Title from PDF title page (viewed July 19, 2017) |
| Beschreibung: | 1 online resource (517 p.) |
| ISBN: | 9789813208933 9813208937 |
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| 520 | |a "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.."--Publisher's website | ||
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| author | Chen, Bang-yen |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| dewey-sort | 3516.3 262 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:51Z |
| institution | BVB |
| isbn | 9789813208933 9813208937 |
| language | English |
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| spelling | Chen, Bang-yen Verfasser aut Differential geometry of warped product manifolds and submanifolds by Bang-Yen Chen Singapore World Scientific Publishing Co. Pte Ltd. c2017 1 online resource (517 p.) txt rdacontent c rdamedia cr rdacarrier Title from PDF title page (viewed July 19, 2017) "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.."--Publisher's website Geometry, Differential Riemannian manifolds Submanifolds Tensor products Electronic books Kähler-Mannigfaltigkeit (DE-588)4162978-4 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Untermannigfaltigkeit (DE-588)4128503-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s Riemannscher Raum (DE-588)4128295-4 s Untermannigfaltigkeit (DE-588)4128503-7 s Kähler-Mannigfaltigkeit (DE-588)4162978-4 s 1\p DE-604 http://www.worldscientific.com/worldscibooks/10.1142/10419#t=toc Verlag URL des Erstveroeffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Chen, Bang-yen Differential geometry of warped product manifolds and submanifolds Geometry, Differential Riemannian manifolds Submanifolds Tensor products Electronic books Kähler-Mannigfaltigkeit (DE-588)4162978-4 gnd Riemannscher Raum (DE-588)4128295-4 gnd Untermannigfaltigkeit (DE-588)4128503-7 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4162978-4 (DE-588)4128295-4 (DE-588)4128503-7 (DE-588)4012248-7 |
| title | Differential geometry of warped product manifolds and submanifolds |
| title_auth | Differential geometry of warped product manifolds and submanifolds |
| title_exact_search | Differential geometry of warped product manifolds and submanifolds |
| title_full | Differential geometry of warped product manifolds and submanifolds by Bang-Yen Chen |
| title_fullStr | Differential geometry of warped product manifolds and submanifolds by Bang-Yen Chen |
| title_full_unstemmed | Differential geometry of warped product manifolds and submanifolds by Bang-Yen Chen |
| title_short | Differential geometry of warped product manifolds and submanifolds |
| title_sort | differential geometry of warped product manifolds and submanifolds |
| topic | Geometry, Differential Riemannian manifolds Submanifolds Tensor products Electronic books Kähler-Mannigfaltigkeit (DE-588)4162978-4 gnd Riemannscher Raum (DE-588)4128295-4 gnd Untermannigfaltigkeit (DE-588)4128503-7 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Geometry, Differential Riemannian manifolds Submanifolds Tensor products Electronic books Kähler-Mannigfaltigkeit Riemannscher Raum Untermannigfaltigkeit Differentialgeometrie |
| url | http://www.worldscientific.com/worldscibooks/10.1142/10419#t=toc |
| work_keys_str_mv | AT chenbangyen differentialgeometryofwarpedproductmanifoldsandsubmanifolds |