Flat surfaces with singularities in Euclidean 3-space

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...

Complete Flat Surfaces with two Isolated Singularities in Hyperbolic 3 - space 1

We construct examples of flat surfaces in H3 which are graphs over a twopunctured horosphere and classify complete embedded flat surfaces in H3 with only one end and at most two isolated singularities. 2000 Mathematical Subject Classification: 53A35, 53C42

Flat surfaces in the hyperbolic 3-space

In this paper we give a conformal representation of flat surfaces in the hyperbolic 3space using the complex structure induced by its second fundamental form. We also study some examples and the behaviour at infinity of complete flat ends. Mathematics Subject Classification (1991): 53A35, 53C42

Minimal Surfaces in Euclidean Space

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...