Aspects of Submanifolds on (α, β)-Type Almost Contact Manifolds with Quasi-Hemi-Slant Factor

In this study, the authors focus on quasi-hemi-slant submanifolds (qhs-submanifolds) of (α,β)-type almost contact manifolds, also known as trans-Sasakian manifolds. Essentially, we give sufficient and necessary conditions for integrability distributions using concept We consider geometry foliations dictated by distribution requirements manifolds with factors to be totally geodesic. Lastly, an illustration a submanifold factor discuss its application number theory.