On some compact Einstein almost Kähler manifolds

Complex Hessian Equations on Some Compact Kähler Manifolds

On a compact connected 2m-dimensional Kähler manifold with Kähler form ω, given a smooth function f : M → R and an integer 1 < k < m, we want to solve uniquely in ω the equation ω̃ ∧ωm−k eω, relying on the notion of k-positivity for ω̃ ∈ ω the extreme cases are solved: k m by Yau in 1978 , and k 1 trivially . We solve by the continuity method the corresponding complex elliptic kthHessian equation...

Ricci Flow on Kähler-einstein Manifolds

A remark on four-dimensional almost Kähler-Einstein manifolds with negative scalar curvature

Concerning the Goldberg conjecture, we will prove a result obtained by applying the result of Iton in terms of L 2-norm of the scalar curvature.

Ricci flow on compact Kähler manifolds of positive bisectional

where ω̃ = ( √ −1/2)g̃ij̄dz ∧ dz and Σ̃ = ( √ −1/2)R̃ij̄dz ∧ dz are the Kähler form, the Ricci form of the metric g̃ respectively, while c1(M) denotes the first Chern class. Under the normalized initial condition (2), the first author [3] (see also Proposition 1.1 in [4]) showed that the solution g(x, t) = ∑ gij̄(x, t)dz dz to the normalized flow (1) exists for all time. Furthermore by the work of Mok ...

Kähler (& Hyper-kähler) Manifolds

These notes are based on two talks given at the Arithmetic & Algebraic Geometry Seminar of the Korteweg-de Vriesinstituut for mathematics of the Universiteit van Amsterdam. They are intended to give a short introduction to the theory of Kähler manifolds, with a slight focus of applicability to the subject of K3 surfaces. However, they also include other interesting results not related to K3 sur...