Mixed product surfaces in euclidean 3-space E^3

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...

Evolution of Translation Surfaces in Euclidean 3-Space E3

Geometry and kinematics have been intimately connected in their historical evolution and, although it is currently less fashionable, the further development of such connections is crucial to many computer-aided design and manufacturing. In this paper, the evolution of the translation surfaces and their generating curves in E3 are investigated. Integrability conditions of the Gauss-Weingarten eq...

Minimal Surfaces in Euclidean Space

Polynomial Translation Weingarten Surfaces in 3-dimensional Euclidean Space

In this paper we will classify those translation surfaces in E involving polynomials which are Weingarten surfaces. Mathematics Subject Classification (2000): 53A05, 53A10.

Structure and characterization of ruled surfaces in Euclidean 3-space

Keywords: Ruled surface Structure function Pitch function Angle function of pitch Weingarten surface Binormal ruled surface a b s t r a c t In this paper, using the elementary method we study ruled surfaces, the simplest foliated submanifolds, in Euclidean 3-space. We define structure functions of the ruled surfaces, the invariants of non-developable ruled surfaces and discuss geometric propert...