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François G. Dorais
François G. Dorais
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All K\"ahlerKähler metrics on a complex manifold?

Let $M$ be a complex manifold of complex dimension 2. What do we know about the set all K"ahlerKähler metrics on $M$ in general and in the case of 4-torus $C^2/Z^4$?

For the case of surfaces ($dim_C=1$), any compatible metric is KahlerKähler and by the uniformization theorem, the answer is that every two such metrics are conformally equivalent and the set all KahlerKähler metrics is nonempty.

All K\"ahler metrics on a complex manifold?

Let $M$ be a complex manifold of complex dimension 2. What do we know about the set all K"ahler metrics on $M$ in general and in the case of 4-torus $C^2/Z^4$?

For the case of surfaces ($dim_C=1$), any compatible metric is Kahler and by the uniformization theorem, the answer is that every two such metrics are conformally equivalent and the set all Kahler metrics is nonempty.

All Kähler metrics on a complex manifold?

Let $M$ be a complex manifold of complex dimension 2. What do we know about the set all Kähler metrics on $M$ in general and in the case of 4-torus $C^2/Z^4$?

For the case of surfaces ($dim_C=1$), any compatible metric is Kähler and by the uniformization theorem, the answer is that every two such metrics are conformally equivalent and the set all Kähler metrics is nonempty.

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Asghar Ghorbanpour
Asghar Ghorbanpour
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All K\"ahler metrics on a complex manifold?

Let $M$ be a complex manifold of complex dimension 2. What do we know about the set all K"ahler metrics on $M$ in general and in the case of 4-torus $C^2/Z^4$?

For the case of surfaces ($dim_C=1$), any compatible metric is Kahler and by the uniformization theorem, the answer is that every two such metrics are conformally equivalent and the set all Kahler metrics is nonempty.