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

Abstract

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 the integrability of distributions using the concept of quasi-hemi-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.

Keywords

• trans-Sasakian manifold
• quasi-hemi-slant submanifold
• totally geodesic
• integrability
• Pontryagin number