Magnetic Curves in Homothetic <i>s</i>-th Sasakian Manifolds

We investigate normal magnetic curves in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mi>s</mi><mo>)</mo></mrow></semantics></math></inline-formula>-dimensional homothetic <i>s</i>-th Sasakian manifolds as a generalization of <i>S</i>-manifolds. We show that a curve <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> is a normal magnetic curve in a homothetic <i>s</i>-th Sasakian manifold if and only if its osculating order satisfies <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>r</mi><mo>≤</mo><mn>3</mn></mrow></semantics></math></inline-formula> and it belongs to a family of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mi>i</mi></msub></semantics></math></inline-formula>-slant helices. Additionally, we construct a homothetic <i>s</i>-th Sasakian manifold using generalized <i>D</i>-homothetic transformations and present the parametric equations of normal magnetic curves in this manifold.