Characterizations of $C$-parallel and $C$-proper $\theta _{i}$-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 $\theta _{i}$-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.