The local classification of Kaehler submanifolds M2n of the hyperbolic space H2n+p with low codimension 2 ≤ p ≤ n − 1 under only intrinsic assumptions remains a wide open problem. The situation is quite different for submanifolds in the round sphere S 2n+p, 2 ≤ p ≤ n − 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 S 3n−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.
Referencia:
Chión Aguirre, S., & Dajczer, M. (2023). Kaehler submanifolds of the real hyperbolic space. Proceedings of the Edinburgh Mathematical Society, 66(3), 810 – 831. https://doi.org/10.1017/S0013091523000445 [Published: August 2023]
