On admissible $f$-rectifying curves in 3D pseudo-Galilean geometry

Abstract

We explore a type of admissible curves in pseudo-Galilean 3-space $\mathbb{G}^1_3$, called $f$-rectifying curves ($f$ being a non-vanishing smooth real-valued function). In $\mathbb{G}^1_3$, a $f$-rectifying curve is presented as an admissible curve $\alpha$ of class at least $C^4$ such that its rectifying planes (spanned by tangent and binormal vectors) entirely contain its $f$-position field $\alpha_f = \int f d\alpha$. We analyse some geometric features of $f$-rectifying curves in $\mathbb{G}^1_3$ as well as in the equiform geometry of $\mathbb{G}^1_3$.

Keywords

• Pseudo-Galilean geometry
• admissible curve
• $f$-rectifying curve
• equiform geometry

Project Number

1

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