Holomorphicity of real Kaehler submanifolds

Alcides de Carvalho, Sergio Chion, Marcos Dajczer

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Let f (Formula Presented) denote an isometric immersion of a Kaehler manifold of complex dimension n ≥ 2 into Euclidean space with codimension p. If the codimension satisfies (Formula Presented), we show that generic rank assumptions on the second fundamental form of the submanifold imply that f has to be a minimal submanifold. In fact, if the codimension is p ≤ 11 we prove that f must be holomorphic with respect to some complex structure in the ambient space.

Original languageEnglish
Pages (from-to)821-837
Number of pages17
JournalAnnali della Scuola Normale Superiore di Pisa - Classe di Scienze
Volume24
Issue number2
DOIs
StatePublished - 2023
Externally publishedYes

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