1 citations · 1 across the 6 of their papers we have counts for
8 papers
Almost-product Kähler surfaces
Andrzej Derdzinski, JeongHyeong Park
We study the case where the tangent bundle of a Kähler surface splits orthogonally into two integrable complex-line subbundles. This amounts to the presence of a unit-length closed…
Scalar-flat Kähler surfaces whose Weyl tensor annihilates the Ricci form
Andrzej Derdzinski, Sinhwi Kim, JeongHyeong Park
We conjecture that any scalar-flat Kähler surface in which the Weyl tensor acting on 2-forms annihilates the Ricci form must be either Ricci-flat or locally isometric to a Riemanni…
Weakly Einstein conformal products
Andrzej Derdzinski, JeongHyeong Park, Wooseok Shin
One says that a Riemannian four-manifold is \emph{weakly Einstein} if the three-index contraction of its curvature tensor against itself equals a function times the metric. Since t…
Weakly Einstein curvature tensors
Andrzej Derdzinski, JeongHyeong Park, Wooseok Shin
We classify weakly Einstein algebraic curvature tensors in an oriented Euclidean 4-space, defined by requiring that the three-index contraction of the curvature tensor against itse…
On weakly Einstein Kähler surfaces
Andrzej Derdzinski, Yunhee Euh, Sinhwi Kim +1
Riemannian four-manifolds in which the triple contraction of the curvature tensor against itself yields a functional multiple of the metric are called weakly Einstein. We focus on…
Affine vector fields on compact pseudo-Kähler manifolds
Andrzej Derdzinski
It is known that a Killing field on a compact pseudo-Kähler manifold is necessarily (real) holomorphic, as long as the manifold satisfies some relatively mild additional conditions…
Harmonic curvature in dimension four
Andrzej Derdzinski
We provide a step towards classifying Riemannian four-manifolds in which the curvature tensor has zero divergence, or -- equivalently -- the Ricci tensor Ric satisfies the Codazzi…
Compact flat manifolds and reducibility
Andrzej Derdzinski, Paolo Piccione
Hiss and Szczepański proved in 1991 that the holonomy group of any compact flat Riemannian manifold, of dimension at least two, acts reducibly on the rational span of the Euclidean…