Quasi-minimal rotational surfaces in pseudo-Euclidean four-dimensional space

Minimal Surfaces in Euclidean Space

Dynamics of Induced Surfaces in Four-Dimensional Euclidean Space

The Davey Stewartson hierarchy will be developed based on a set of three matrix differential operators. These equations will act as evolution equations for different types of surface deformation in Euclidean four space. The Weierstrass representation for surfaces will be developed and its uniqueness up to gauge transformations will be reviewed. Applications of the hierarchy will be given with r...

Smooth surfaces in three-dimensional Euclidean space

are locally described by classical differential geometry. In case some spatial direction (e.g., the direction of gravity in the natural landscape or the viewing direction in visual space) assumes a special role, this formalism has to be replaced by the special theory of “topographic surfaces’’ and one speaks of “surface relief ’’ (Liebmann, 1902/1927). Examples include topographic relief and— i...

Characterizations of Slant Ruled Surfaces in the Euclidean 3-space

In this study, we give the relationships between the conical curvatures of ruled surfaces generated by the unit vectors of the ruling, central normal and central tangent of a ruled surface in the Euclidean 3-space E^3. We obtain differential equations characterizing slant ruled surfaces and if the reference ruled surface is a slant ruled surface, we give the conditions for the surfaces generate...

Linear Weingarten Rotational Surfaces in Pseudo-Galilean 3-Space

In the present paper, we study rotational surfaces in the three dimensional pseudo-Galilean space G3. Also, we classify linear Weingarten rotational surfaces in G3. A linear Weingarten surface is the surface having a linear equation between the Gaussian curvature and the mean curvature of a surface. In last section, we construct isotropic rotational surfaces in G3 with prescribed mean curvature...