Higher order parallel surfaces in three-dimensional homogeneous spaces

dc.creatorVan der Veken, Joeri
dc.date2006-04-25
dc.date2008-02-08
dc.date.accessioned2026-07-07T09:19:21Z
dc.date.available2026-07-07T09:19:21Z
dc.descriptionWe 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 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.
dc.descriptionTo appear under the title "Higher order parallel surfaces in Bianchi-Cartan-Vranceanu spaces" in Result. Math. (in press)
dc.identifierhttps://arxiv.org/abs/math/0604541
dc.identifierhttp://arxiv.org/abs/math/0604541
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154359
dc.subjectDifferential Geometry
dc.subject53B25 (Primary), 53C40 (Secondary)
dc.titleHigher order parallel surfaces in three-dimensional homogeneous spaces
dc.typetext

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