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Sung Yeon, Kim
복소기하학 연구단
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Totally geodesic discs in bounded symmetric domains

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Title
Totally geodesic discs in bounded symmetric domains
Author(s)
Sung-Yeon Kim; Seo, Aeryeong
Publication Date
2022-09
Journal
Complex Analysis and its Synergies, v.8, no.3
Publisher
Springer International Publishing
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.
URI
https://pr.ibs.re.kr/handle/8788114/12209
DOI
10.1007/s40627-022-00098-z
ISSN
2524-7581
Appears in Collections:
Center for Complex Geometry (복소기하학 연구단) > 1. Journal Papers (저널논문)
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