On Spacelike Rotational Surfaces With Pointwise 1-Type Gauss Map

Abstract

Abstract. In this paper, we study a class of spacelike rotational surfaces in the Minkowski 4-space E 4 1 with meridian curves lying in 2-dimensional spacelike planes and having pointwise 1-type Gauss map. We obtain all such surfaces with pointwise 1-type Gauss map of the first kind. Then we prove that the spacelike rotational surface with flat normal bundle and pointwise 1-type Gauss map of the second kind is an open part of a spacelike 2-plane in E 4 1 .

General Rotational Surfaces in Pseudo-Euclidean 4-Space with Neutral Metric

“…Similarly to the general rotations in the Euclidean space E 4 one can consider general rotational surfaces in the Minkowski 4-space E 4 1 (see [11] and [6]). Now we shall define general rotational surfaces of Moore type in the pseudo-Euclidean 4-space E 4 2 .…”

“…The classification of minimal general rotational surfaces in E 4 1 and general rotational surfaces consisting of parabolic points is also given in [11]. Spacelike general rotational surfaces in E 4 1 with meridian curves lying in 2-dimensional planes and having pointwise 1-type Gauss map are studied in [6].…”

Tubular Surface Having Pointwise 1-type Gauss Map in Euclidean 4-Space

“…Otherwise, second kind [14]. Surfaces satisfying (1.2) have been the subject of many studies such as [1,15,16,17,21,22,26,27]. In recent years, authors deal with the meridian surfaces with pointwise 1-type Gauss map in some spaces in [2,3].…”

Rotational Surfaces with Pointwise 1-Type Gauss Map in Pseudo Euclidean Space $\mathbb{E}_{2}^{4}$

“…for some smooth function f on M and some constant vector C. A submanifold of a Euclidean space or pseudo-Euclidean space is said to have pointwise 1-type Gauss map, if its Gauss map satisfies (1) for some smooth function f on M and some constant vector C. If the vector C in (1) is zero, a submanifold with pointwise 1-type Gauss map is said to be of the first kind, otherwise it is said to be of the second kind. A lot of papers were recently published about rotational surfaces with pointwise 1-type Gauss map in four dimensional Euclidean and pseudo Euclidean space in [1], [3], [4], [8], [9] [11].Timelike and spacelike rotational surfaces of elliptic, hyperbolic and parabolic types in Minkowski space E 4 1 with pointwise 1-type Gauss map were studied in [5,7]. Aksoyak and Yaylı in [2] studied boost invariant surfaces (rotational surfaces of hyperbolic type) with pointwise 1-type Gauss map in Minkowski space E 4 1 .…”

“…A lot of papers were recently published about rotational surfaces with pointwise 1-type Gauss map in four dimensional Euclidean and pseudo Euclidean space in [1], [3], [4], [8], [9] [11].Timelike and spacelike rotational surfaces of elliptic, hyperbolic and parabolic types in Minkowski space E 4 1 with pointwise 1-type Gauss map were studied in [5,7]. Aksoyak and Yaylı in [2] studied boost invariant surfaces (rotational surfaces of hyperbolic type) with pointwise 1-type Gauss map in Minkowski space E 4 1 .…”