Real Kaehler submanifolds in codimension up to four

• Sergio Chion Aguirre ^[1] ; Marcos Dajczer ^[2]
  1. [1] Pontificia Universidad Católica del Perú

     Pontificia Universidad Católica del Perú

     Perú

     
  2. [2] Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 39, Nº 6, 2023, págs. 2331-2348
• Idioma: inglés
• DOI: 10.4171/RMI/1427
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• Resumen

  • Let f:M2n→R2n+4 be an isometric immersion of a Kaehler manifold of complex dimension n≥5 into Euclidean space with complex rank at least 5 everywhere. Our main result is that, along each connected component of an open dense subset of M2n, either f is holomorphic in R2n+4≅Cn+2, or it is in a unique way a composition f=F∘h of isometric immersions. In the latter case, we have that h:M2n→N2n+2 is holomorphic and F:N2n+2→R2n+4 belongs to the class, by now quite well understood, of non-holomorphic Kaehler submanifolds in codimension two. Moreover, the submanifold F is minimal if and only if f is minimal.