Tag: Sung Yeon Kim

In this talk, we study the rigidity of proper holomorphic maps f: Ω→Ω‘​​ between irreducible bounded symmetric domains Ω​​ and Ω‘​​. First, we will define the moduli maps induced by f​​. This moduli maps are CR maps between real orbits in flag maniflods. If the rank difference is small, i.e., 2 ≤ rank(Ω‘)< 2 rank(Ω)-1​​, then there exists a moduli map which preserves the VMRT structures on the real orbits. Using this property, we will show that f: Ω → Ω‘​​ is a holomorphic totally geodesic isometric embedding with respect to Kobayashi metrics for certain pairs (Ω, Ω‘)​​. This is a joint work with N. Mok and A. Seo.

Let G​ be a complex semisimple Lie group, P​​ be a parabolic subgroup and G⁰​​ be a real form of G.​​ Then the flag manifold G/P​​ decomposes into finitely many G⁰-orbits. The complex structure of G/P​​ yields a natural homogeneous CR manifold structure on the real orbits such that all elements in G⁰ are CR automorphisms. Among them there is exactly one orbit of minimal dimension, which is compact. Shilov boundary of bounded symmetric domains are the well-known examples of such minimal orbits. In this talk, we study real orbits from the point of view of CR geometry. In particular we study the CR structures on the minimal orbits in Grassmannians.