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arXiv · 1810.06968

Conformally flat submanifolds with flat normal bundle

Marcos Dajczer·Christos-Raent Onti·Theodoros Vlachos
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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.

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Marcos Dajczer, Christos-Raent Onti, Theodoros Vlachos. 2018-10-16. Conformally flat submanifolds with flat normal bundle. https://arxiv.org/abs/1810.06968

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