Some Surfaces with Zero Curvature in ℍ

We study surfaces defined as graph of the function z=f(x,y) in the product space ℍ2×ℝ. In particular, we completely classify flat or minimal surfaces given by f(x,y)=u(x)+v(y), where u(x) and v(y) are smooth functions

Surfaces of revolution in the three dimensional pseudo-Galilean space

In the present paper, we study surfaces of revolution in the three dimensional pseudo-Galilean space G31 . Also, we characterize surfaces of revolution in G31 in terms of the position vector field and Gauss map

The evolution of the electric field along optical fiber for the type-2 and 3 PAFs in Minkowski 3-space

In this paper, we introduce the type-2 and the type-3 Positional Adapted Frame(PAF) of spacelike curve and timelike curve in Minkowski 3-space. From these PAFs, we study the evolutions of the electric field vectors of the type-2 and type-3 PAFs. As a result, we also investigate the Fermi-Walker parallel and the Lorentz force equation of the electric field vectors for the type-2 and type-3 PAFs in Minkowski 3-space

CHARACTERIZATIONS OF NORMAL AND BINORMAL SURFACES IN G3

In this paper, our aim is to give surfaces in the Galilean 3-space G3 with the property that there exist four geodesics through each point such that every surface built with the normal lines and the binormal lines along these geodesics is a surface with a minimal surface and a constant negative Gaussian curvature. We show that should be an isoparametric surface in G3: A plane or a circular hyperboloid

MANNHEIM CURVES IN AN N-DIMENSIONAL LORENTZ MANIFOLD

In this paper, we give the definition of non-null Mannheim curve and null Mannheim curve in an n-dimensional Lorentz manifold. Furthermore, we give the condition for the non-null Mannheim partner curves and the null Mannhein partner curves

CLASSIFICATION OF ROTATIONAL SURFACES IN PSEUDO-GALILEAN SPACE

In the present paper, we study rotational surfaces in the three dimensional pseudo-Galilean space G31 . Also, we characterize rotational surfaces in G31 in terms of the position vector field, Gauss map and Laplacian operator of the second fundamental form on the surface

Timelike General Rotational Surfaces in Minkowski 4-Space with Density

In this study, we give weighted mean and weighted Gaussian curvatures of two types of timelike general rotational surfaces with non-null plane meridian curves in four-dimensional Minkowski space E^4_1 with density e^({\lambda}_1x^2+{\lambda}_2^y2+{\lambda}_3z^2+{\lambda}_4t^2), where {\lambda}_i (i = 1,2,3,4) are not all zero and we give some results about weighted minimal and weighted flat timelike general rotational surfaces in E^4_1 with density. Also, we construct some examples for these surfaces.Comment: 16 pages, 3 figure