Yüca, Gülsüm2021-05-032021-05-032021https:/dx.doi.org/10.1016/j.geomphys.2021.104139https://hdl.handle.net/20.500.12451/7927The dual transformation between Lie groups is given in Dohi et al. (2010). In this study, a new dual transformation is defined between Lie algebras of Lie groups, allows us to obtain semi-orthogonal matrices from skew-symmetric matrices. This transition is represented by a commutative diagram. Afterward, the study is carried into dual spaces. Additionally, a new method for obtaining two surfaces which share the same curve is described. It is provided with applications and their figures are drawn in E-3 and E-1(3). Geometric and physical interpretations are also given.eninfo:eu-repo/semantics/openAccessSkew-symmetric MatricesSemi-orthogonal matricesCayley TransformationDual TransformationKinematicsArticle163---10.1016/j.geomphys.2021.104139Q1WOS:000636084800006Q2