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| | Hello! <br>My name is Mariana and I'm a 27 years old boy from United States.<br><br>Here is my page :: [http://samdal.pe.kr/xe/baekpa_board/1057498 Bookbyte Sell Coupon] |
| {{Expert-subject|Mathematics|date=November 2008}}
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| {{Refimprove|date=May 2010}}
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| In [[mathematics]] and [[physics]], in particular [[differential geometry]] and [[general relativity]], a '''warped geometry''' is a [[Riemannian manifold|Riemannian]] or [[Lorentzian manifold]] whose metric tensor can be written in form
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| :<math>ds^2 \, = g_{ab}(y) \, dy^a \, dy^b + f(y) g_{ij}(x) \, dx^i \, dx^j. </math>
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| Note that the geometry almost decomposes into a [[Cartesian product]] of the ''y'' geometry and the ''x'' geometry – except that the ''x''-part is warped, i.e. it is rescaled by a scalar function of the other coordinates ''y''. For this reason, the metric of a warped geometry is often called a warped product metric.<ref>
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| {{cite book|first=Bang-Yen|last=Chen|title=Pseudo-Riemanniann geometry, [delta]-invariants and applications|publisher=World Scientific|year=2011|isbn=978-981-4329-63-7}}</ref><ref>{{cite book|first=Barrett|last=O'Neill|title=Semi-Riemanniann geometry|publisher=Academic Press|year=1983|isbn=0-12-526740-1}}</ref>
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| Warped geometries are useful in that [[separation of variables]] can be used when solving [[partial differential equation]]s over them.
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| ==Examples==
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| Warped geometries acquire their full meaning when we substitute the variable ''y'' for ''t'', time and ''x'', for ''s'', space. Then the ''d''(''y'') factor of the spatial dimension becomes the effect of time that in words of Einstein 'curves space'. How it curves space will define one or other solution to a space-time world. For that reason different models of space-time use warped geometries.
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| Many basic solutions of the [[Einstein field equations]] are warped geometries, for example the [[Schwarzschild solution]] and the [[Friedmann–Lemaître–Robertson–Walker metric|Friedmann–Lemaitre–Robertson–Walker models]].
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| Also, warped geometries are the key building block of [[Randall–Sundrum model]]s in [[particle physics]].
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| ==See also==
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| * [[Metric tensor]]
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| * [[Exact solutions in general relativity]]
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| * [[Poincaré half-plane model]]
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| ==References==
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| {{Reflist}}
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| [[Category:Differential geometry]]
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| [[Category:General relativity]]
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| {{differential-geometry-stub}}
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| {{Relativity-stub}}
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Hello!
My name is Mariana and I'm a 27 years old boy from United States.
Here is my page :: Bookbyte Sell Coupon