1 citations · 1 across the 11 of their papers we have counts for
12 papers
Rigidity of compact four-dimensional weakly Einstein Ricci Solitons
JeongHyeong Park, Wooseok Shin
We prove that every compact four-dimensional weakly Einstein Ricci soliton is Einstein. The nontrivial compact case reduces to the gradient shrinking setting, where a differential…
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…
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…
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…
On weakly Einstein Lie groups
Yunhee Euh, Sinhwi Kim, Yuri Nikolayevsky +1
A Riemannian manifold is called \emph{weakly Einstein} if the tensor is a scalar multiple of the metric tensor . We consider weakly Einstein Lie gro…
Weakly Einstein hypersurfaces in space forms
Jihun Kim, Yuri Nikolayevsky, JeongHyeong Park
A Riemannian manifold is called \emph{weakly Einstein} if the tensor is a scalar multiple of the metric tensor . We give a complete classifi…
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 submanifolds in space forms satisfying certain equalities
Jihun Kim, JeongHyeong Park
We classify weakly Einstein submanifolds in space forms that satisfy Chen's equality. We also give a classification of weakly Einstein hypersurfaces in space forms that satisfy the…
Asymptotically harmonic manifolds of dimension 3 with minimal horospheres
Jihun Kim, JeongHyeong Park, Hemangi Madhusudan Shah
In [14], it was shown that, if M is a 3-dimensional asymptotically harmonic with minimal horospheres, then M is flat. However, there is a gap in the proof of this paper. In this pa…