A Characterization of Factorable Surfaces in Euclidean 4-Space E^4

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...

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...

Special Bertrand Curves in semi-Euclidean space E4^2 and their Characterizations

In [14] Matsuda and Yorozu.explained that there is no special Bertrand curves in Eⁿ and they new kind of Bertrand curves called (1,3)-type Bertrand curves Euclidean space. In this paper , by using the similar methods given by Matsuda and Yorozu [14], we obtain that bitorsion of the quaternionic curve is not equal to zero in semi-Euclidean space E4^2. Obtain (N,B2) type quaternionic Bertrand cur...

A characterization of curves in Galilean 4-space $G_4$

‎In the present study‎, ‎we consider a regular curve in Galilean‎ ‎$4$-space $mathbb{G}_{4}$ whose position vector is written as a‎ ‎linear combination of its Frenet vectors‎. ‎We characterize such‎ ‎curves in terms of their curvature functions‎. ‎Further‎, ‎we obtain‎ ‎some results of rectifying‎, ‎constant ratio‎, ‎$T$-constant and‎ ‎$N$-constant curves in $mathbb{G}_{4}$‎.

Minimal Surfaces in Euclidean Space