General Rotational Surfaces with Pointwise 1-Type Gauss Map in Pseudo- Euclidean Space E42

In this paper, we study general rotational surfaces in the 4- dimensional pseudo-Euclidean space E4-2 and obtain a characterization of flat general rotation surfaces with pointwise 1-type Gauss map in E4-2 and give an example of such surfaces.Comment: arXiv admin note: substantial text overlap with arXiv:1302.280

Quaternıonic Bertrand Curves Accordıng To Type 2-Quaternıonıc Frame In R-4

In this paper, we give some characterizations of quaternionic Bertrand curves whose torsion is non-zero but bitorsion is zero in R-4 according to Type 2-Quaternionic Frame. One of the most important points in working on quaternionic curves is that given a curve in R-4, the curve in R-3 associated with this curve is determined individually. So, we obtain some relationships between quaternionic Bertrand curve alpha((4)) in R(4)and its associated spatial quaternionic curve alpha in R-3. Also, we support some theorems in the paper by means of an example

Generalized Bicomplex Numbers and Lie Groups

In this paper, we denone the generalized bicomplex numbers and give some algebraic properties of them. Also, we show that some hyperquadrics in R4 and R42 are Lie groups by using generalized bicomplex number product and obtain Lie algebras of these Lie groups. Morever, by using tensor product surfaces, we determine some special Lie subgroups of these hyperquadrics.Comment: thank yo

Flat Rotational Surfaces with Pointwise 1-Type Gauss Map Via Generalized Quaternions

In this paper,we determine a rotational surface by means of generalized quaternions and study this flat rotational surface with pointwise 1-type Gauss map in four-dimensional generalized space Eαβ4. Also, for some special cases of α and β, we obtain the characterizations of flat rotational surfaces with pointwise 1-type Gauss map in four-dimensional Euclidean space E4 and four-dimensional pseudo-Euclidean space E24. © 2018, The National Academy of Sciences, India

Characterizations of Loxodromes on Rotational Surfaces in Euclidean 3–Space

In this paper, we study on the characterizations of loxodromes on the rotational surfaces satisfying some special geometric properties such as having constant Gaussian curvature and a constant ratio of principal curvatures (CRPC rotational surfaces). First, we give the parametrizations of loxodromes parametrized by arc-length parameter on any rotational surfaces in E 3 and then, we calculate the curvature and the torsion of such loxodromes. Then, we give the parametrizations of loxodromes on rotational surfaces with constant Gaussian curvature. Also, we investigate the loxodromes on the CRPC rotational surfaces. Moreover, we give the parametrizations of loxodromes on the minimal rotational surface which is a special case of CRPC rotational surfaces. Finally, we give some visual examples to strengthen our main results via Wolfram Mathematica 10.4