Kaehler submanifolds of the real hyperbolic space

Chion S.; Dajczer M. · Proceedings of the Edinburgh Mathematical Society (2023) · DOI: 10.1017/s0013091523000445

Resumen

The local classification of Kaehler submanifolds of the hyperbolic space with low codimension under only intrinsic assumptions remains a wide open problem. The situation is quite different for submanifolds in the round sphere, since Florit et al. [7] have shown that the codimension has to be and then that any submanifold is just part of an extrinsic product of two-dimensional umbilical spheres in. 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]. © The Author(s), 2023. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

Instituciones: Pontificia Universidad Católica del Perú