Kaya, Filiz Ertem2024-11-072024-11-0720220037-87122175-1188https://doi.org/10.5269/bspm.46768https://hdl.handle.net/11480/15016We find a geometric invariant of the curve-surface pairs on Willmore functions with the mean and Gauss curvatures. Similar to the work in [5,19], in this work, we define Willmore functions on curve-surface pair and give new characterizations about Willmore functions with necessary and sufficient condition with strip theory in Euclidean 3-space for the first time. In this paper Willmore function on curvatures of the curve-surface pair under Mobius transformation is provided invariant.eninfo:eu-repo/semantics/openAccessCurve-surface pairmobius transformationcurvatureWillmore functionArticle4010.5269/bspm.467682-s2.0-85124154530Q3WOS:000834220200038N/A