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yyoon@fas.harvard.edu
science forum beginner
Joined: 05 May 2006
Posts: 2
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 Posted: Fri May 05, 2006 8:14 pm Post subject:
sasaki-einstein manifold
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Why is Sasaki-Einstein manifold named so?
Did Sasaki and Einstein come out with this idea?
I am just curious. |
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Aaron Bergman
science forum addict
Joined: 24 Mar 2005
Posts: 94
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| Posted: Sat May 20, 2006 1:19 am Post subject:
Re: sasaki-einstein manifold
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In article <1146745977.855257.31540@j73g2000cwa.googlegroups.com>,
yyoon@fas.harvard.edu wrote:
| Quote: | Why is Sasaki-Einstein manifold named so?
Did Sasaki and Einstein come out with this idea?
I am just curious.
|
There's such a thing as a Sasakian manifold, and there's such a thing as
an Einstein manifold. A Sasaki-Einstein manifold is one that is both.
Sasaki is, in a sense, an odd dimensional version of a Kaehler manifold.
An Einstein manifold is a solution to the Einstein field equations with
a cosmological constant. In other words, the Ricci tensor is
proportional to the metric.
The string theory relevance here is that the base of a Ricci flat cone
is Einstein and the base of a Kaehler cone is Sasaki. Thus, the base of
a Calabi-Yau cone is Sasaki-Einstein.
Aaron |
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Igor
science forum Guru
Joined: 15 May 2005
Posts: 315
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| Posted: Sat May 20, 2006 1:19 am Post subject:
Re: sasaki-einstein manifold
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yyoon@fas.harvard.edu wrote:
| Quote: | Why is Sasaki-Einstein manifold named so?
Did Sasaki and Einstein come out with this idea?
I am just curious.
|
I'm not sure that it applies to this particular case, but the term
Einstein manifold usually relates to vacuum solutions to the GR
equations with a non-zero cosmological constant. The name seems to be
used more often in pure math literature rather than physics. |
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