8 papers
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…
Critical metrics for the quadratic curvature functional on complete four-dimensional manifolds
Yunhee Euh, JeongHyeong Park
We study critical metrics of the curvature functional $\A(g)=\int_M |R|^2\, \vol$, on complete four-dimensional Riemannian manifolds with finite energy, that is, $\A(g)<\in…
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…
Horospherical mean curvature functions and D'Atri spaces
Gerhard Knieper, JeongHyeong Park, Norbert Peyerimhoff
We consider simply connected Riemannian manifolds without conjugate points for which the horospherical mean curvature function is continuous, reversible and invariant under the geo…
Higher order obstructions to Riccati-type equations
Jihun Kim, Paul-Andi Nagy, JeongHyeong Park
We develop new techniques in order to deal with Riccati-type equations, subject to a further algebraic constraint, on Riemannian manifolds . We find that the obstruction t…
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…