Surfaces inE 4 with a Gaussian curvature coinciding with a Gaussian torsion up to the sign

Inflection points and asymptotic lines on Lagrangian surfaces

“…Then, using these formulae or those from [1,2], we obtain the following expressions for the Gaussian and normal curvature: Proposition 1. The Gaussian curvature is given by:…”

“…The vector field: ( ẋ, ẏ) = (a+c, e+g) = ((ζ 1 +ζ 3 )x+(ζ 2 +ζ 4 )y, (ζ 2 +ζ 4 )x+(ζ 3 +ζ 5 )y)+O (2) spans the direction h, and therefore ind h is +1 or −1 as the determinant:…”

A study on self-similar surfaces

“…Especially, curvature properties are used for obtaining textural features in pattern recognition and image segmentation [14,15]. On the other hand, some special surfaces in E 4 such as generalized rotating surfaces [10], Lawson surfaces [16], Aminow surfaces [1], Vranceanu surfaces [20], flat Klein bottle [19], Banchoff surfaces [6], Loop surfaces [12], tensor product surfaces [17], meridian surfaces [11] are important the differential geometry of surfaces.…”

On the pedal surfaces of 2-d surfaces with the constant support function in E^4

“…The study of surfaces in higher dimensions have also been studied by many authors (see, e.g. [1,3,5] E .…”

“…The following figures of surfaces are drawn by using parallel projection. Example 1: Let 1 N and 2 N be the unit normal vectors of surface M given with the Monge patch:…”