Our goal in this review study is to provide a thorough and mostly self-contained description of semi-symmetric non-metric connections on Kenmotsu manifolds. Kenmotsu manifolds are a special class of nearly contact metric manifold, also an interesting classis of nearly contact structures that has relevance in the differential geometry itself due to its rich geometrical nature and several theoretical and practical applications. This means that classical Riemannian geometry can be generalized in such a way that we make the condition of metric compatibility less strict, while still having some aspects of torsion retained.
The main objective of this review is to explain some basic concepts from all these angles based on fundamental definitions and features coming from curvature tensors as well the Ricci and scalar behaviors, invariance conditions; with strong innovations in the field. We focus on the case of some Gauduchon-type metrics as Ricci solitons, η-Einstein manifolds and different curvature tensors. In addition, the provided survey emphasizes important results and open challenges along with promising directions for future studies.