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<p>The aim of this paper is to investigate properties of non-Newtonian (multiplicative) evolutes and involutes of multiplicative fronts in the multiplicative Euclidean plane. Firstly, we give the definitions of multiplicative evolute curve and multiplicative involute curve without multiplicative inflection points. Even though a multiplicative curve is multiplicative regular, the multiplicative evolute and involute can still exhibit singularities. Then we introduce the multiplicative Legendre curves and multiplicative Legendre immersion. Under the above notions, we define a multiplicative evolute and a multiplicative involute of the multiplicative front. We also give relationship between multiplicative evolutes and involutes of multiplicative fronts without multiplicative inflection points. Next, we extend them to <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(r_*\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mi>r</mi> <mrow> <mrow /> <mo>∗</mo> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>-th. Finally, we present an example to demonstrate the main results.</p>

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Non-Newtonian evolutes and involutes of multiplicative fronts in the multiplicative Euclidean plane

  • 期刊论文

  • 发表日期：

    2025年9月4日

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  • Xinyu Yao,
  • Haiming Liu,
  • Naijin Yuan

摘要

The aim of this paper is to investigate properties of non-Newtonian (multiplicative) evolutes and involutes of multiplicative fronts in the multiplicative Euclidean plane. Firstly, we give the definitions of multiplicative evolute curve and multiplicative involute curve without multiplicative inflection points. Even though a multiplicative curve is multiplicative regular, the multiplicative evolute and involute can still exhibit singularities. Then we introduce the multiplicative Legendre curves and multiplicative Legendre immersion. Under the above notions, we define a multiplicative evolute and a multiplicative involute of the multiplicative front. We also give relationship between multiplicative evolutes and involutes of multiplicative fronts without multiplicative inflection points. Next, we extend them to \(r_*\) r ∗ -th. Finally, we present an example to demonstrate the main results.