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1. A complex manifold carrying a Kähler–Einstein metric.
2. A compact simply connected homogeneous Kähler manifold, called a Kähler C-space, carries a Kähler–Einstein metric with positive scalar curvature and has the structure of a Kähler–Einstein manifold.
3. Moreover, the following obstructions to the existence of Kähler–Einstein metrics are known (cf.
4. For more examples, see Kähler–Einstein manifold.
5. In a) and b) there is always a Kahler-Einstein metric by a theorem of Aubin and Yau.
6. In general the question weather a given Kahler surface admits an Einstein metric is quite subtle.
7. "Every compact, simply connected, homogeneous Kahler manifold admits a unique (up to homothety) invariant Kahler-Einstein metric structure"- this result can be found in Y. Matsushima.
8. A manifold is said to be Kähler–Einstein if it admits a Kähler–Einstein metric.
9. The most important problem for this area is the existence of Kähler–Einstein metrics for compact Kähler manifolds.
10. if and only if it is locally product (globally, if the manifold is simply connected and complete) of Kahler-Einstein metrics.
11. In the final section we shall prove the uniqueness up to equivalence of Kahler-Einstein metrics in a simply connected compact com- plex homogeneous space.
12. There exists a section 5 = SL of E such that KAHLER-EINSTEIN MANIFOLDS 165 <SX, F> = K(X, ) for all X, Y e (T).
13. The existence of a Kähler-Einstein metric when the curvature is negative or flat is known, thanks to the celebrated work of Aubin and Yau.
14. Due to the pioneering work of Donaldson et al, the existence of a Kähler-Einstein metric in this case is determined by an algebraic stability condition on the underlying Fano variety.
15. Our results extend to many other types of canonical metrics in Kahler geometry aside from Kahler-Einstein metrics.
16. In the 90's, Tian conjectured an analytic characterization of Kahler-Einstein metrics.
17. Tian also conjectured a Kahler-Einstein analogue of the well-known Aubin-Moser-Trudinger inequality in conformal geometry.
18. These classes contain Ricci-flat metrics, which in the limit collapse to a twisted Kahler-Einstein metric on the base (away from the singular fibers).
19. In this paper, we consider a generalized Kahler-Einstein equation on Kahler manifold M .
20. Complex Monge-Amp`ere equation, energy functional, generalized Kahler-Einstein metric, Moser-Trudinger type inequality.
21. 1 2 XI ZHANG AND XIANGWEN ZHANG (1.1) will be called by a generalized Kahler-Einstein metric.
22. In this paper, we consider the remained case k > 0, there should be obstructions to admit generalized Kahler-Einstein metrics.
23. Our main result is: Let N^2n be a Kahler-Einstein manifold with positive scalar curvature with an effective T^n-action.
24. This chapter discusses the recent progress on Kahler-Einstein manifolds.
25. It explores a brand new non-linear inequality on compact Kahler-Einstein manifolds.
26. The chapter establishes the stability of the underlying manifold if there is a Kahler-Einstein metric using previous result on the connection between Kahler-Einstein metrics and stability.
27. More than forty years ago, E. Calabi asked if a compact Kahler manifold M admits any Kahler-Einstein metrics.
28. An important recent development in geometry has been the announcement of two claimed proofs of a long-standing conjecture about the existence of Kähler-Einstein metrics.
29. Then we use continuity method to study the deformation of weak conical Kahler-Einstein metric on Q-Fano variety.
30. During the period of our joint project on the Kahler-Einstein problem on Fano variety, they gave me very patient and friendly tutoring on both algebraic geometry and dieren- tial geometry.
31. If M admits a Kahler-Einstein metric with positive scalar cur- vature, then M is weakly K-stable.
32. Then M has a Kahler-Einstein metric if and only if M is weakly K-stable in the sense of Denition 1.1.

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Spacy 패턴 목록

• [{'LOWER': 'kahler'}, {'OP': '*'}, {'LOWER': 'einstein'}]
• [{'LOWER': 'kähler'}, {'OP': '*'}, {'LOWER': 'einstein'}, {'LOWER': 'manifold'}]
• [{'LOWER': 'kähler'}, {'OP': '*'}, {'LOWER': 'einstein'}, {'LEMMA': 'metric'}]