Holomorphicity of totally geodesic Kobayashi isometry between bounded symmetric domains

초록

In this paper, we study the holomorphicity of totally geodesic Kobayashi isometric embeddings between bounded symmetric domains. First we show that for a C-1-smooth totally geodesic Kobayashi isometric embedding f:Omega ->Omega ' where Omega, Omega ' are bounded symmetric domains, if Omega is irreducible and rank(Omega)>= rank(Omega ') or more generally, rank(Omega)>= rank(f & lowast;v) for any tangent vector v of Omega, then f is either holomorphic or anti-holomorphic. Secondly we characterize C-1 Kobayashi isometries from a reducible bounded symmetric domain to itself.

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