Spacelike Rotational Surfaces of Elliptic, Hyperbolic and Parabolic Types in Minkowski Space E 1 4 ${E^{4}_{1}}$ with Pointwise 1-Type Gauss Map

Timelike rotational surfaces of elliptic, hyperbolic and parabolic types in Minkowski space E41 with pointwise 1-type Gauss map

“…Let M 2 be a timelike rotational surface of hyperbolic type in E defined by (10). Without loss of generality, we assume that the smooth timelike profile curve β is parametrized by its arc lenght s, i.e.,…”

“…On the other hand, using the Codazzi equation (5) we get e 1 (h defined by (10). Suppose that the principal direction β (s) is nonnull.…”

“…Moreover, in [15] a complete classification of cylindrical and non-cylindrical surfaces in E m 1 with pointwise 1-type Gauss map of the first kind was obtained. Recently, the authors studied rotational spacelike surfaces of elliptic, hyperbolic and parabolic types in E 4 1 , [10]. In this article, we focus on a class of timelike rotational surfaces in Minkowski space E 4 1 with 2-dimensional axis.…”

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 .…”

Surfaces of Revolution With Pointwise 1-Type Gauss Map in Pseudo-Galilean Space

“…A helicoid, a catenoid and a right cone are the typical examples of surfaces with pointwise 1-type Gauss map. Many results of submanifolds with pointwise 1-type Gauss map were obtained in [1], [3], [5], [6], [7], [9], [12], etc, when the ambient spaces are the Euclidean space, Minkowski space and Galilean space.…”