Riemann solitons on almost co-Kähler manifolds

Riemann Poisson Manifolds and Kähler-riemann Foliations

1 Riemann Poisson manifolds were introduced by the author in [1] and studied in more details in [2]. Kähler-Riemann foliations form an interesting subset of the Riemannian foliations with remarkable properties ( see [3]). In this paper we will show that to give a regular Riemann Poisson structure on a manifold M is equivalent to to give a Kähler-Riemann foliation on M such that the leafwise sym...

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...

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.

Torsion in Almost Kähler Geometry *

We study almost Kähler manifolds whose curvature tensor satisfies the second curvature condition of Gray (shortly AK 2). This condition is interpreted in terms of the first canonical Hermitian connection. It turns out that this condition forces the torsion of this connection to be parallel in directions orthogonal to the Kähler nullity of the almost complex structure. We prove a local structure...

0 Ricci flow on Kähler manifolds