Totally geodesic discs in bounded symmetric domains

초록

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 <inf>1</inf> and Ω <inf>2</inf> of Ω ′ such that f= (f<inf>1</inf>, f<inf>2</inf>) maps into Ω <inf>1</inf>× Ω <inf>2</inf>⊂ Ω where f<inf>1</inf> is holomorphic and f<inf>2</inf> is anti-holomorphic totally geodesic isometric embeddings. If rank (Ω ′) < 2 rank (Ω) , then either f or f¯ is a standard holomorphic embedding. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

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