2022/02/11 by Kim, Sung-Yeon, Seo, Aeryeong · 1 citation
#Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2202.05473
In this paper, we study the holomorphicity of totally geodesic Kobayashi isometric embeddings between bounded symmetric domains. First we show that for a C1-smooth totally geodesic Kobayashi isometric embedding f\colon Ω→Ω' where Ω, Ω' are bounded symmetric domains, if Ω is irreducible and rank(Ω) ≥ rank(Ω') or more generally, rank(Ω) ≥ rank(f_*v) for any tangent vector v of Ω, then f is either holomorphic or anti-holomorphic. Secondly we characterize C1 Kobayashi isometries from a reducible bounded symmetric domain to itself.