Conformally flat submanifolds with flat normal bundle
Differential Geometry
2019-10-15 v2
Abstract
We prove that any conformally flat submanifold with flat normal bundle in a conformally flat Riemannian manifold is locally holonomic, that is, admits a principal coordinate system. As one of the consequences of this fact, it is shown that the Ribaucour transformation can be used to construct an associated large family of immersions with induced conformal metrics holonomic with respect to the same coordinate system.
Cite
@article{arxiv.1810.06968,
title = {Conformally flat submanifolds with flat normal bundle},
author = {Marcos Dajczer and Christos-Raent Onti and Theodoros Vlachos},
journal= {arXiv preprint arXiv:1810.06968},
year = {2019}
}