Meridian Surfaces in E^4 with Pointwise 1-type Gauss Map
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Publication:2901327
zbMATH Open1247.53009arXiv1410.7907MaRDI QIDQ2901327
Kadri Arslan, Velichka Milousheva, Betül Bulca
Publication date: 19 July 2012
Abstract: In the present article we study a special class of surfaces in the four-dimensional Euclidean space, which are one-parameter systems of meridians of the standard rotational hypersurface. They are called meridian surfaces. We show that a meridian surface has a harmonic Gauss map if and only if it is part of a plane. Further, we give necessary and sufficient conditions for a meridian surface to have pointwise 1-type Gauss map and find all meridian surfaces with pointwise 1-type Gauss map.
Full work available at URL: https://arxiv.org/abs/1410.7907
Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40)
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