NOTES ON SURFACES WITH CONSTANT GAUSS CURVATURE ALONG A CURVE IN THE LIE GROUP - Yuzbasi, Zuhal Kucukarslan; Şahin, Gamze Köse (My University, 2022)
In this paper, the linear combination of the Lie Frenet frame of a given curve is used to create a parametric surface family. Using the coefficients of the surface's first and second fundamental forms, the Gauss curvature of this parametric surface is determined. Also, sufficient conditions for the surface when its Gauss curvature is constant along the given curve are derived. Moreover, sufficient conditions are found when the finding surface is a ruled surface, as a member of the family. Finally, a few examples to support our theory are created in the Lie group.
Keywords: Surfaces; Lie group; Gauss curvature