Warped product pointwise PR-semi-slant immersions in para-Kähler manifolds

This study investigates the geometry of warped product pointwise PR-semi- slant immersions M in para-Kahler manifolds M̄2m that naturally englobes the warped product PR and semi-slant immersions. We first derive the non-existence of warped product Mλ ×f MT, and then by presenting a numerical example examine the presence of warped product M such that M = MT ×fMλ in M̄2m. Finally, we derive some characterizations for pointwise PR-semi-slant submanifolds to be locally warped product MT ×f Mλ in terms of shape operator and endomorphisms. The mixed totally geodesic case is also discussed.