Holomorphicity of real Kaehler submanifolds

de Carvalho A.; Chion S.; Dajczer M. · Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2023) · DOI: 10.2422/2036-2145.202105_013

Resumen

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.

Instituciones: Pontificia Universidad Católica del Perú