1-Lightlike surfaces in semi-Euclidean 4-space with index two

1-Lightlike surfaces in semi-Euclidean 4-space with index two

By establishing some differential geometry theory on the 1-lightlike surfaces, we show several geometric properties of the 1-lightlike surfaces which are completely different from non-lightlike surfaces. Based on these theories, we consider the singularities of the 1-lightlike surfaces in semiEuclidean 4-space with index two as an application of the theory of Legendrian singularities. We charac...

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...

On the Quaternionic Curves in the Semi-Euclidean Space E_4_2

In this study, we investigate the semi-real quaternionic curves in the semi-Euclidean space E_4_2. Firstly, we introduce algebraic properties of semi-real quaternions. Then, we give some characterizations of semi-real quaternionic involute-evolute curves in the semi-Euclidean space E42 . Finally, we give an example illustrated with Mathematica Programme.

Minimal Surfaces in Euclidean Space

Parallel Transport Frame in 4 -dimensional Euclidean Space

In this work, we give parallel transport frame of a curve and we introduce the relations between the frame and Frenet frame of the curve in 4-dimensional Euclidean space. The relation which is well known in Euclidean 3-space is generalized for the …rst time in 4-dimensional Euclidean space. Then we obtain the condition for spherical curves using the parallel transport frame of them. The conditi...