On the Geometry of Semi-Slant Submanifolds in Kenmotsu Manifolds endowed with the Schouten-van Kampen Connection

The main objective of this paper is to investigate the geometry of semi-slant submanifolds in Kenmotsu manifolds defined with respect to the Schouten-van Kampen connection. Unlike the Levi-Civita connection, the Schouten-van Kampen connection offers a more rigid geometric framework where the structure vector field ξ and the metric tensor remain parallel. In this study, we first establish the existence of semi-slant submanifolds in this setting and obtain necessary and sufficient conditions for their characterization. Furthermore, we investigate the integrability conditions of the invariant and slant distributions associated with the semi-slant structure. We derive new results concerning the total geodesicity of these submanifolds and the geometric properties of the induced connection. Finally, we provide a non-trivial example of a 5-dimensional semi-slant submanifold in ℝ⁷ to illustrate the theoretical results obtained.