INNER PRODUCT STRUCTURES AND E. STUDY MAPS ON DUAL SPACES - Yuce, Salim; Kolay, Maide (HONAM MATHEMATICAL SOC, 2025)
In the literature, fundamental and algebraic operations on the set of dual numbers were studied. The set of dual numbers was discussed as considering a inner product space and the E. Study map was also investigated [5,7, 14, 19,21]. Additionally, geometric and mechanical scientists examined the E. Study map in many spaces. In this study, a new inner product space is obtained by using the Galilean inner product in the space D-n. We aim to extend the investigation of dual numbers and the E. Study map to the context of Galilean space. Building upon the existing research, we work to explore the application of the E. Study map in this unique geometric setting. Our focus is to develop a suitable inner product for Galilean space and utilize it to prove the E. Study map in this framework.
Keywords: dual vector; inner product; Galilean inner product; E. Study map; SURFACES; VECTORS; NUMBERS; Mathematics