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.  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  for spherical submanifolds. Besides, we generalize several results obtained by Dajczer and Vlachos.
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]