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Bull. Korean Math. Soc. 2014; 51(3): 911-922
Printed May 31, 2014
https://doi.org/10.4134/BKMS.2014.51.3.911
Copyright © The Korean Mathematical Society.
Meridian surfaces in $\mathbb{E}^{4}$ with pointwise 1-type Gauss map
Kadri Arslan, Bet\"{u}l Bulca, and Velichka Milousheva
Uluda\u{g} University, Uluda\u{g} University, ``L. Karavelov" Civil Engineering Higher School
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
MSC numbers: 53A07, 53C40, 53C42
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