Holomorphicity of totally geodesic Kobayashi isometry between bounded symmetric domains

2024/03/01 by Sung‐Yeon Kim, Aeryeong Seo · 3 citations
Mathematics · #Holomorphic and Operator Theory #Geometry and complex manifolds #Analytic and geometric function theory

paper · doi:10.1112/jlms.12882

Abstract

Abstract In this paper, we study the holomorphicity of totally geodesic Kobayashi isometric embeddings between bounded symmetric domains. First, we show that for a ‐smooth totally geodesic Kobayashi isometric embedding where , are bounded symmetric domains, if is irreducible and or more generally, for any tangent vector of , then is either holomorphic or anti‐holomorphic. Second, we characterize Kobayashi isometries from a reducible bounded symmetric domain to itself.

Cited by

• Rigidity of Kobayashi isometries of a class of 2-dimensional Lempert manifolds
• Carathéodory distance-preserving maps between bounded symmetric domains
• Isometries in the diamond

Related

• Holomorphicity of totally geodesic Kobayashi isometry between bounded symmetric domains
• Totally geodesic discs in strongly convex domains
• Remarks on holomorphic isometric embeddings between bounded symmetric domains
• Totally geodesic discs in bounded symmetric domains
• Isometric disks are holomorphic