이재혁 교수

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.

For 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.

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.