Rigidity for local holomorphic isometric embeddings from bn into bn1 × ⃛ × bnm up to conformal factors

Yuan Yuan, Yuan Zhang

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

In this article, we study local holomorphic isometric embeddings from bn into bn1 × ⃛ × bnm with respect to the normalized Bergman metrics up to conformal factors. Assume that each conformal factor is smooth Nash algebraic. Then each component of the map is a multi-valued holomorphic map between complex Euclidean spaces by the algebraic extension theorem derived along the lines of Mok, and Mok and Ng. Applying holomorphic continuation and analyzing real analytic subvarieties carefully, we show that each component is either a constant map or a proper holomorphic map between balls. Applying a linearity criterion of Huang, we conclude the total geodesy of non-constant components.

Original languageEnglish (US)
Pages (from-to)329-349
Number of pages21
JournalJournal of Differential Geometry
Volume90
Issue number2
DOIs
StatePublished - Jan 1 2012
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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