Rafael López, Ana Nistor
Published 2014-10-09Version 1
In this paper we study surfaces foliated by a uniparametric family of circles in the homogeneous space Sol$_3$. We prove that there do not exist such surfaces with zero mean curvature or with zero Gaussian curvature. We extend this study considering surfaces foliated by geodesics, equidistant lines or horocycles in totally geodesic planes and we classify all such surfaces under the assumption of minimality or flatness.
Journal: Results in Mathematics, 64 (2013), No. 3-4, 319-330
Hypersurfaces with Light-Like Points in a Lorentzian Manifold II
Timelike surfaces with zero mean curvature in Minkowski 4-space
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