Open AccessWillmore function on curvatures of the curve-surface pair under mobius transformation
Author(s) -
Filiz Ertem Kaya
Publication year - 2022
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.46768
Subject(s) - willmore energy , mathematics , invariant (physics) , mathematical analysis , surface (topology) , gaussian curvature , euclidean geometry , second fundamental form , euclidean space , principal curvature , transformation (genetics) , function (biology) , mean curvature , geometry , pure mathematics , curvature , mathematical physics , biochemistry , chemistry , evolutionary biology , biology , gene
We 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 Möbiüs transformation is provided invariant.