Balanced Metrics and Noncommutative Kähler Geometry
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...
Збережено в:
| Дата: | 2010 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2010
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146504 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Balanced Metrics and Noncommutative Kähler Geometry / S. Lukic // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 23 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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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