Semi-symmetric metric connections and homology of warped product pointwise semi-slant submanifolds in a Kaehler manifold admitting a concurrent vector field

In this paper, we delve into the study of pointwise semi-slant submanifolds in a Kaehler manifold using a semi-symmetric metric connection within the framework of warped product geometry. Our investigation yields fundamental and significant results that shed light on the properties of these submanifolds. Furthermore, we explore the implications of our findings for the homology of these submanifolds, providing insights into their topological characteristics. Specifically, we establish a compelling proof that, subject to a specific condition, stable currents do not exist for these warped product pointwise semi-slant submanifolds. The outcomes of our research contribute substantial knowledge regarding the stability and behavior of warped product pointwise semi-slant submanifolds equipped with a semi-symmetric metric connection. Moreover, this work establishes a solid foundation for future investigations and advancements in this field of study.