6 papers
Hypersurfaces with constant sectional curvature of a product of two space forms
Jihun Kim, Yuri Nikolayevsky, Ruy Tojeiro
We complete the classification of hypersurfaces with constant sectional curvature of dimension greater than or equal to three in the product of two space forms.
Phase Retrieval in Requires Exactly Eleven Measurements
Meng Huang, Jihun Kim
Determining the minimal number of intensity measurements required for phase retrieval in has been a long-standing open problem. Prior to this work, the best-known re…
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…