Totally geodesic discs in bounded symmetric domains

In this paper, we characterize C 2 -smooth totally geodesic isometric embeddings f : Ω → Ω ′ between bounded symmetric domains Ω and Ω ′ which extend C 1 -smoothly over some open subset in the Shilov boundaries and have nontrivial normal derivatives on it. In particular, if Ω is irreducible, there e...

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Vydané v:	Complex analysis and its synergies Ročník 8; číslo 3
Hlavní autori:	Kim, Sung-Yeon, Seo, Aeryeong
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Cham Springer International Publishing 01.09.2022 Springer Nature B.V
Predmet:	Algebraic Geometry Analysis Domains Dynamical Systems and Ergodic Theory Functional Analysis Functions of a Complex Variable Mappings and symmetry in complex and CR geometry Mathematical analysis Mathematics Mathematics and Statistics Partial Differential Equations 32M15 53C35 Totally geodesic isometric embedding 53C55 Bounded symmetric domain Holomorphicity Bergman metric
ISSN:	2524-7581, 2197-120X
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Popis
Shrnutí:	In this paper, we characterize C 2 -smooth totally geodesic isometric embeddings f : Ω → Ω ′ between bounded symmetric domains Ω and Ω ′ which extend C 1 -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 = ( f 1 , f 2 ) maps into Ω 1 × Ω 2 ⊂ Ω where f 1 is holomorphic and f 2 is anti-holomorphic totally geodesic isometric embeddings. If rank ( Ω ′ ) < 2 rank ( Ω ) , then either f or f ¯ is a standard holomorphic embedding.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	2524-7581 2197-120X
DOI:	10.1007/s40627-022-00098-z