On Inverse of a Regular Surface With Respect to the Unit Sphere S2 in E3

Abstract

The purpose of this paper, first, is to give a definition of the inverse surface of a given regular surface with respect to a unit sphere in E3. Second, some characteristic properties of the inverse surface are to express depending on the algebraic invariants of the original surface. In the last part of the study, we gave examples supporting our claims and plotted their graphics with the help of Maple software program.

Geometry of the Focal Surfaces of the Inverse Surface of a Regular Surface in E3

“…Ottens studied geometry of Dupin cyclides under the inversion transformation [14] S rı ğ ug Kuru ğ u, g r ur [15,16]. Tul et al investigated inverse surface of a regular surface with respect to the unit sphere and found some new characteristic properties of its [17]. Furthermore, the inverse surface studied by Röthe [18].…”