| 词条 | Constant scalar curvature Kähler metric |
| 释义 |
In differential geometry, a constant scalar curvature Kähler metric (cscK metric), is (as the name suggests) a Kähler metric on a complex manifold whose scalar curvature is constant. A special case is Kähler-Einstein metric, and a more general case is extremal Kähler metric. {{harvtxt|Donaldson|2002}}, Tian {{Citation needed|date=January 2019}} and Yau {{Citation needed|date=January 2019}} conjectured that the existence of a cscK metric on a polarised projective manifold is equivalent to the polarised manifold being K-polystable. Recent developments in the field suggest that the correct equivalence may be to the polarised manifold being uniformly K-polystable {{Citation needed|date=January 2019}}. When the polarisation is given by the (anti)-canonical line bundle (i.e. in the case of Fano or Calabi-Yau manifolds) the notions of K-stability and K-polystability coincide, cscK metrics are precisely Kähler-Einstein metrics and the Yau-Tian-Donaldson conjecture is known to hold {{Citation needed|date=January 2019}}.References
1 : Complex manifolds |
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