Balanced Metrics and Noncommutative Kähler Geometry
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Balanced Metrics and Noncommutative Kähler Geometry
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| Creator |
Lukic, S.
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| Description |
In this paper we show how Einstein metrics are naturally described using the quantization of the algebra of functions C∞(M) on a Kähler manifold M. In this setup one interprets M as the phase space itself, equipped with the Poisson brackets inherited from the Kähler 2-form. We compare the geometric quantization framework with several deformation quantization approaches. We find that the balanced metrics appear naturally as a result of requiring the vacuum energy to be the constant function on the moduli space of semiclassical vacua. In the classical limit, these metrics become Kähler-Einstein (when M admits such metrics). Finally, we sketch several applications of this formalism, such as explicit constructions of special Lagrangian submanifolds in compact Calabi-Yau manifolds.
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| Date |
2019-02-09T19:31:39Z
2019-02-09T19:31:39Z 2010 |
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| Type |
Article
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| Identifier |
Balanced Metrics and Noncommutative Kähler Geometry / S. Lukic // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 23 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 14J32; 32Q15; 32Q20; 53C25; 53D50 doi:10.3842/SIGMA.2010.069 http://dspace.nbuv.gov.ua/handle/123456789/146504 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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