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Title: Higher order parallel surfaces in Bianchi-Cartan-Vranceanu spaces
Authors: Van der Veken, Joeri # ×
Issue Date: Mar-2008
Series Title: Results in mathematics vol:51 issue:3-4 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 2002. 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 parametrization of all totally umbilical surfaces.
ISSN: 1422-6383
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Geometry Section
× corresponding author
# (joint) last author

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