Abstract

The 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 E3 and E13. Geometric and physical interpretations are also given.

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