Artículos académicos Real Kaehler submanifolds in codimension up to four

Real Kaehler submanifolds in codimension up to four

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Autoría

Año de publicación

2023

Palabras clave

Variedades de Kahler, Teoría de cuerdas

Título en español

Subvariedades reales de Kaehler en codimensión hasta cuatro

Let f ⁣:M2n→R2n+4f:M2n→R2n+4 be an isometric immersion of a Kaehler manifold of complex dimension n≥5n≥5 into Euclidean space with complex rank at least 55 everywhere. Our main result is that, along each connected component of an open dense subset of M2nM2n, either ff is holomorphic in R2n+4≅Cn+2R2n+4≅Cn+2, or it is in a unique way a composition f=F∘hf=F∘h of isometric immersions. In the latter case, we have that h ⁣:M2n→N2n+2h:M2n→N2n+2 is holomorphic and F ⁣:N2n+2→R2n+4F:N2n+2→R2n+4 belongs to the class, by now quite well understood, of non-holomorphic Kaehler submanifolds in codimension two. Moreover, the submanifold FF is minimal if and only if ff is minimal.

Referencia

Chion, S. & Dajczer, M. (2023). Real Kaehler submanifolds in codimension up to four. Revista Matemática Iberoamericana. Advanced online publication. DOI 10.4171/RMI/1427 Real Kaehler submanifolds in codimension up to four

Sergio Julio Chión Aguirre

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