ϵ-isothermic surfaces in pseudo-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...

Stationary isothermic surfaces and some characterizations of the hyperplane in the N - dimensional Euclidean space ∗

We consider an entire graph S of a continuous real function over R N−1 with N ≥ 3. Let Ω be a domain in RN with S as a boundary. Consider in Ω the heat flow with initial temperature 0 and boundary temperature 1. The problem we consider is to characterize S in such a way that there exists a stationary isothermic surface in Ω. We show that S must be a hyperplane under some general conditions on S...

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...

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.