Abstract

The Möbius transformation is known as a part of analysis and mostly studied by the researchers and scientist who made their investigations on analysis. But in this paper it is worked together with differential geometry. It is well known that harmonic curvature  of the curve  is found by Hacısalihoglu and also harmonic curvatures  and  of the curve-surface pair that we call the strip as shown as  is studied by Hacısalihoglu and Ertem Kaya. We observe the image of the harmonic curvatures  and  of the curve-surface pair  in differential geometry under Möbius transformation in analysis. We find the images of  harmonic curvatures  and  of the strip  by the help of the Möbius transformation. Consequently, in this paper the curvatures and the harmonic curvature  of the curve-surface pair under Möbius transformation is studied and  is not invariant for Möbius transformation is obtained.

Key words: Curve-surface pair, Möbius transformation, curvature.