# MERIDIAN SURFACES IN 𝔼4 WITH POINTWISE 1-TYPE GAUSS MAP

• Arslan, Kadri (Department of Mathematics Uludag University) ;
• Bulca, Betul (Department of Mathematics Uludag University) ;
• Milousheva, Velichka (Bulgarian Academy of Sciences Institute of Mathematics and Informatics, "L. Karavelov" Civil Engineering Higher School)
• Published : 2014.05.31
• 145 6

#### 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.

#### Keywords

Meridian surfaces;Gauss map;finite type immersions;pointwise 1-type Gauss map

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