ON EINSTEIN, HERMITIAN 4-MANIFOLDS Claude LeBrun

For k > p, L −k minus the zero section admits a gradient expanding soliton such that the corresponding K¨ ahler-Ricci flow g(t) converges to a Ricci-flat K¨ ahler cone metric

Theorem A Let M be a four-dimensional K¨ ahler-Einstein manifold, then a symplectic surface remains symplectic along the mean curvature flow and the flow does not develop any type

In an unpub- lished paper, Perelman proved that the scalar curvature and diameter are always uniformly bounded along the K¨ ahler-Ricci flow, and he announced that if there exists a

Finally we remark that for each d ∈ { 1, 2, 3, 4 } , it is easy to find explicit examples of singular degree d Q -Gorenstein smoothable K¨ ahler-Einstein log Del Pezzo surface by

Tian [Tia9] proved that there is a K¨ ahler-Einstein metric if and only if the K-energy is proper on the space of all K¨ ahler metrics in c 1 (X).. So the problem is how to test

(Although it is not stated explicitly in [13], it is clear that the power m in that case also depends only on the dimension of X i , λ and the positive lower bound of Ricci

A Riemannian version of the celebrated Goldberg-Sachs theorem of Gen- eral Relativity implies that a Riemannian Einstein 4-manifold locally admits a positively oriented

We prove there (Corollary 3 and Proposition 6) that, except for some trivial cases, self-dual Kâhler metrics coincide, locally, with (four-dimensional) metrics of