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Sasaki-Einstein structures and their compactification Gover, Rod
Description
Sasaki geometry is often viewed as an odd dimensional analogue of Kaehler geometry. In particular a Riemannian or pseudo-Riemannian manifold is Sasakian if its standard metric cone is Kaehler or, respectively, pseudo-Kaehler. We show that there is a natural link between Sasaki geometry and projective differential geometry. The situation is particularly elegant for Sasaki-Einstein geometries and in this setting we use projective geometry to provide the resolution of these geometries into â less rigidâ components. This is analogous to usual picture of a Kaehler structure: a symplectic manifold equipped also with a compatible complex structure etc. However the treatment of Sasaki geometry this way is locally more interesting and involves the projective Cartan or tractor connection. This enables us to describe a natural notion of compactification for complete non-compact pseudo-Riemannian Sasakian geometries. For such compactifications the boundary at infinity is a conformal manifold with a Fefferman space structureâ so it fibres over a CR manifold. This is nicely compatible with the compactification of the Kaehler-Einstein manifold that arises, in the usual way, as a leaf space for the defining Killing field of the given Sasaki-Einstein manifold. This is joint work with Katharina Neusser and Travis Willse.
Item Metadata
Title |
Sasaki-Einstein structures and their compactification
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2018-05-14T11:38
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Description |
Sasaki geometry is often viewed as an odd dimensional analogue of Kaehler geometry. In particular a Riemannian or pseudo-Riemannian manifold is Sasakian if its standard metric cone is Kaehler or, respectively, pseudo-Kaehler. We show that there is a natural link between Sasaki geometry and projective differential geometry. The situation is particularly elegant for Sasaki-Einstein geometries and in this setting we use projective geometry to provide the resolution of these geometries into â less rigidâ components. This is analogous to usual picture of a Kaehler structure: a symplectic manifold equipped also with a compatible complex structure etc. However the treatment of Sasaki geometry this way is locally more interesting and involves the projective Cartan or tractor connection. This enables us to describe a natural notion of compactification for complete non-compact pseudo-Riemannian Sasakian geometries. For such compactifications the boundary at infinity is a conformal manifold with a Fefferman space structureâ so it fibres over a CR manifold. This is nicely compatible with the compactification of the Kaehler-Einstein manifold that arises, in the usual way, as a leaf space for the defining Killing field of the given Sasaki-Einstein manifold.
This is joint work with Katharina Neusser and Travis Willse.
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Extent |
54.0
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Auckland
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Series | |
Date Available |
2019-03-21
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0377271
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International