MERIDIAN SURFACES IN E-4 WITH POINTWISE 1-TYPE GAUSS MAP


ARSLAN K., BULCA B., Milousheva V.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.51, no.3, pp.911-922, 2014 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 3
  • Publication Date: 2014
  • Doi Number: 10.4134/bkms.2014.51.3.911
  • Journal Name: BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.911-922
  • Keywords: Meridian surfaces, Gauss map, finite type immersions, pointwise 1-type Gauss map, RULED SURFACES

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.