Characterizations of c-parallel and c-proper θ i-slant curves in homothetic s-th sasakian manifolds

Abstract

This paper explores C-parallel and C-proper curves within the tangent and normal bundles of homothetic s-th Sasakian manifolds. We establish the necessary and sufficient conditions for θi-slant curves to belong to these specific classes. To solidify our theoretical results, we present three concrete examples using parametric equations on a homothetic s-th Sasakian manifold, each satisfying the derived theorems.