SPACELIKE TRANSLATION SURFACES IN MINKOWSKI 4-SPACE E_1^4

In the present paper, we consider spacelike translation surfaces in $4$-dimensio\-nal Minkowski space. We characterize such surfaces in terms of their Gaussian curvature and mean curvature functions. We classify flat and minimal spacelike translation surfaces in $\mathbb{E}_{1}^{4}$.

A new type timelike surface given with monge patch in E41

In this work, we think about timelike Aminov surface of hyperbolic type in four dimensional Minkowski space E⁴₁. We investigate and classify this surface with respect to its Gaussian curvature, mean curvature and normal curvature. We get some results on flat, minimal and semiumbilical hyperbolic type Aminov surfaces. Further, we obtain necessary and sufficient condition for this type of surface to become Wintgen Ideal Surface in Minkowski space-time.Publisher's Versio

A NEW CHARACTERIZATION OF CURVES IN MINKOWSKI 4-SPACE E_1^4

In this study, we attend to the curves whose position vectors are written as alinear combination of their Serret-Frenet vectors in Minkowski 4-Space E_1^4. We characterize such curves with regard to their curvatures. Further, we get certain consequences of T-constant and N-constant types of curves in E_1^4.

Some characteristic properties of AW (k)-type curves on dual unit sphere

In this paper, we have considered some properties of AW (k)-type curves on the dual unit sphere. We have given some relationships between the curvatures of the base curves of the ruled surfaces in ℝ³which correspond to the dual spherical curves of these type. And also, we have examined the relations between the real integral invariants (the angle of pitch and the pitch) of the closed ruled surfaces in ℝ³ which correspond to the dual closed spherical curves drawn by the dual unit vectors (N₁) ⃗ , (N₂) ⃗ and (N₃) ⃗on dual unit sphere.peerReviewe

Some characteristic properties of AW (k)-type curves on dual unit sphere

In this paper, we have considered some properties of AW (k)-type curves on the dual unit sphere. We have given some relationships between the curvatures of the base curves of the ruled surfaces in ℝ³which correspond to the dual spherical curves of these type. And also, we have examined the relations between the real integral invariants (the angle of pitch and the pitch) of the closed ruled surfaces in ℝ³ which correspond to the dual closed spherical curves drawn by the dual unit vectors (N₁) ⃗ , (N₂) ⃗ and (N₃) ⃗on dual unit sphere.peerReviewe

On translation surfaces in 4-dimensional Euclidean space

We consider translation surfaces in Euclidean spaces. Firstly, we give some results of translation surfaces in the 3-dimensional Euclidean space E3. Further, we consider translation surfaces in the 4-dimensional Euclidean space E4. We prove that a translation surface is flat in E4 if and only if it is either a hyperplane or a hypercylinder. Finally we give necessary and sufficient condition for a quadratic triangular Bézier surface in E4 to become a translation surface