Discussion:
sasaki-einstein manifold
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y***@fas.harvard.edu
2006-05-05 20:14:26 UTC
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Why is Sasaki-Einstein manifold named so?
Did Sasaki and Einstein come out with this idea?
I am just curious.
Aaron Bergman
2006-05-20 01:19:09 UTC
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Post by y***@fas.harvard.edu
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
Igor
2006-05-20 01:19:26 UTC
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Post by y***@fas.harvard.edu
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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