Artículos académicos Kaehler submanifolds of the real hyperbolic space

Kaehler submanifolds of the real hyperbolic space

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Año de publicación

2023

Palabras clave

hyperbolic space Kaehler submanifolds

Título en español

Subvariedades de Kaehler del espacio hiperbólico real

The local classification of Kaehler submanifolds M2n of the hyperbolic space H2n+p with low codimension 2≤pn−1 under only intrinsic assumptions remains a wide open problem. The situation is quite different for submanifolds in the round sphere S2n+p, 2≤pn−1, since Florit et al. [7] have shown that the codimension has to be p=n−1 and then that any submanifold is just part of an extrinsic product of two-dimensional umbilical spheres in S3n−1⊂R3n. The main result of this paper is a version for Kaehler manifolds isometrically immersed into the hyperbolic ambient space of the result in [7] for spherical submanifolds. Besides, we generalize several results obtained by Dajczer and Vlachos [5].

Sergio Julio Chión Aguirre

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