Meridian Surfaces of Elliptic or Hyperbolic Type with Pointwise 1-type Gauss Map in Minkowski 4-space

In the present paper we consider a special class of spacelike surfaces in the Minkowski 4-space which are one-parameter systems of meridians of the rotational hypersurface with timelike or spacelike axis. They are called meridian surfaces of elliptic or hyperbolic type, respectively. We study these...

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Published inTaiwanese journal of mathematics Vol. 20; no. 2; pp. 311 - 332
Main Authors Arslan, Kadri, Milousheva, Velichka
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.04.2016
Subjects
Axes of rotation
Curvature
Euclidean space
Hypersurfaces
Mathematical constants
Mathematical surfaces
Mathematical vectors
Minkowski space
Tangents
Vector fields
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Summary:In the present paper we consider a special class of spacelike surfaces in the Minkowski 4-space which are one-parameter systems of meridians of the rotational hypersurface with timelike or spacelike axis. They are called meridian surfaces of elliptic or hyperbolic type, respectively. We study these surfaces with respect to their Gauss map. We find all meridian surfaces of elliptic or hyperbolic type with harmonic Gauss map and give the complete classification of meridian surfaces of elliptic or hyperbolic type with pointwise 1-type Gauss map. 2010Mathematics Subject Classification. Primary: 53A35; Secondary: 53B20, 53B25. Key words and phrases. Meridian surfaces in Minkowski space, Finite type immersions, Harmonic Gauss map, Pointwise 1-type Gauss map.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.20.2016.5722