Componentwise rigidity of holomorphic isometric maps between bounded symmetric domains with negative conformal factors

Abstract

Let $D$ be an irreducible bounded symmetric domain of complex dimension at least two. We study local holomorphic maps from $D$ into products of irreducible bounded symmetric domains satisfying a metric identity with positive and negative conformal factors. Under a noncancellation condition on these factors, we prove that every nonconstant component extends to a holomorphic isometric embedding up to a positive integer factor. This proves a componentwise rigidity conjecture formulated by Cheng--Hao--Yuan--Zhang.

arXiv commentSubstantially expanded and revised: the new results now cover general irreducible bounded symmetric source domains and allow negative conformal factors. Now 27 pages