# Higher Order Parallel Surfaces in Bianchi–Cartan–Vranceanu Spaces

@article{Veken2008HigherOP, title={Higher Order Parallel Surfaces in Bianchi–Cartan–Vranceanu Spaces}, author={Joeri Van der Veken}, journal={Results in Mathematics}, year={2008}, volume={51}, pages={339-359} }

Abstract.We give a full classification of higher order parallel surfaces in three-dimensional homogeneous spaces with four-dimensional isometry group, i.e., in the so-called Bianchi–Cartan–Vranceanu family. This gives a positive answer to a conjecture formulated in [2]. As a partial result, we prove that totally umbilical surfaces only exist if the ambient Bianchi–Cartan–Vranceanu space is a Riemannian product of a surface of constant Gaussian curvature and the real line, and we give a local… Expand

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