Totally geodesic discs in bounded symmetric domains

Sung Yeon Kim, Aeryeong Seo

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we characterize C2-smooth totally geodesic isometric embeddings f: Ω → Ω between bounded symmetric domains Ω and Ω which extend C1-smoothly over some open subset in the Shilov boundaries and have nontrivial normal derivatives on it. In particular, if Ω is irreducible, there exist totally geodesic bounded symmetric subdomains Ω 1 and Ω 2 of Ω such that f= (f1, f2) maps into Ω 1× Ω 2⊂ Ω where f1 is holomorphic and f2 is anti-holomorphic totally geodesic isometric embeddings. If rank (Ω ) < 2 rank (Ω) , then either f or f¯ is a standard holomorphic embedding.

Original languageEnglish
Article number10
JournalComplex Analysis and its Synergies
Volume8
Issue number3
DOIs
StatePublished - Sep 2022

Keywords

  • Bergman metric
  • Bounded symmetric domain
  • Holomorphicity
  • Totally geodesic isometric embedding

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