Lee Jae-Hyuk
Ewha Womans University
About the Lab
Professor Lee Jae-Hyuk's research lab specializes in differential geometry and geometric analysis, with a focus on symplectic geometry, Lagrangian submanifolds, and isoparametric systems. The lab investigates the interplay between geometric structures—such as symplectic and Stenzel forms—and submanifolds in spheres and projective spaces, particularly through the lens of special Lagrangian and austere submanifolds. A central theme is the construction and classification of isoparametric hypersurfaces in spheres and quaternionic projective spaces using invariant homogeneous functions. The lab also explores deformation theory and geometric transitions, such as the deformation of symplectic Grassmannians to complex Grassmannians.
Research Overview
Research Output Trend
Figures are computed from collected data and may differ slightly.
Selected Papers
4For each submanifold X in the sphere S(n), we show that the correspond-ing conormal bundle N(*) is Lagrangian for the Stenzel form on T(*)S(n). Furthermore,we correspond an austere submanifold X to a special Lagrangian submanifold N¤X in T¤Sn. We also discuss austere submanifolds in Sn from isoparametric geometry.
We introduce a decomposition on a symplectic subspace determined by symplectic structure and study its properties. As a consequence, we give an elementary proof of the deformation of the Grassmannians of symplectic subspaces to the complex Grassmannians.
In this article, we consider a homogeneous function of degree four in quaternionic vector spaces and S^(4n+3) which is invariant under S^3 and U(n + 1)-action. We show it is an isoparametric function providing isoparametric hypersurfaces in S^(4n+3) with g = 4 distinct principal curvatures and isoparametric hypersurfaces in quaternionic projective spaces with g = 5. This extends study of Nomizu on isoparametric function on complex vector spaces and complex projective spaces.
Dive deeper into Lee Jae-Hyuk's research on Nubint
Open this lab's papers in the app to read with AI, summarize, and cite in your writing.