A four-dimensional example of a Ricci flat metric admitting almost-Kähler non-Kähler structure

ADIABATIC LIMITS OF RICCI - FLAT KÄHLER METRICS 3 from

We study adiabatic limits of Ricci-flat Kähler metrics on a Calabi-Yau manifold which is the total space of a holomorphic fibration when the volume of the fibers goes to zero. By establishing some new a priori estimates for the relevant complex Monge-Ampère equation, we show that the Ricci-flat metrics collapse (away from the singular fibers) to a metric on the base of the fibration. This metri...

The Scalar-flat Kähler Metric and Painlevé Iii

We study the anti-self-dual equation for non-diagonal SU(2)-invariant metrics and give an equivalent ninth-order system. This system reduce to a sixth-order system if the metric is in the conformal class of scalar-flatKähler metric.

Gravity as a Nonholonomic Almost Kähler

A geometric procedure is elaborated for transforming (pseudo) Riemanian metrics and connections into canonical geometric objects (metric and nonlinear and linear connections) for effective Lagrange, or Finsler, geometries which, in their turn, can be equivalently represented as almost Kähler spaces. This allows us to formulate an approach to quantum gravity following standard methods of deforma...

Ricci Flow on Kähler-einstein Surfaces

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.