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Joeri Van der Veken

Publications and source records attributed to Joeri Van der Veken.

39 records · Page 3Linked to original sources
arXiv2008

Higher order parallel surfaces in three-dimensional homogeneous spaces

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 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.

math.DG↗
arXiv2007

Remarks on an inequality involving the normal scalar curvature

We study a pointwise inequality for submanifolds in real space forms involving the scalar curvature, the normal scalar curvature and the mean curvature. We translate it into an algebraic problem, allowing us to prove a slightly weaker version of it. We also prove the conjecture for certain types of submanifolds of $\mathbb C^n$.

math.DG↗