Let f W M2n ! R2nCp denote an isometric immersion of a Kaehler manifold of complex dimension n � 2 into Euclidean space with codimension p. If the codimension satisfies 2p 2n � 1, 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.
De Carvalho, A., Chion, S. & Dajczer, M. (2023). Holomorphicity of real Kaehler submanifolds. The Annali della Scuola Normale Superiore di Pissa, Classe di Scienze, 24(2), 821-837. https://doi.org/10.2422/2036-2145.202105_013 Recuperado de: https://journals.sns.it/index.php/annaliscienze/article/view/5753