Abstract

The purpose of this paper is to introduce a new class of admissible curves, referred to as $f$-rectifying curves, and study their geometric properties in Galilean 3-space $\mathbb{G}_3$. For some non-vanishing real-valued smooth function $f$, an $f$-rectifying curve in $\mathbb{G}_3$ is introduced as an admissible curve $\gamma$ of class at least $C^4$ such that its $f$-position vector field, given by $\gamma_f = \int f d\gamma$, lies on its rectifying planes (i.e., the planes generated by its tangent and binormal vectors). Some geometric characterizations of such curves are explored in $\mathbb{G}_3$. Moreover, they are investigated in the equiform geometry of $\mathbb{G}_3$.

Keywords: Galilean geometry; admissible curve; $f$-rectifying curve; equiform geometry.

MSC: 53A35, 53A40, 53B25, 53C40

DOI: 10.57016/MV-FKQg1328

Pages:  245--256     

Volume  76 ,  Issue  4 ,  2024