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

Automated summary

In this study, the authors investigate quasi-hemi-slant submanifolds in trans-Sasakian manifolds. They provide necessary and sufficient conditions for the integrability of distributions using quasihemi-slant submanifolds. The authors also analyze the geometric properties of foliations dictated by the distributions and discuss the requirements for quasi-hemi-slant factors to be totally geodesic in submanifolds of trans-Sasakian manifolds. Lastly, they illustrate the application of a submanifold with a quasi-hemi-slant factor in number theory.