On the Topology of Warped Product Pointwise Semi-Slant Submanifolds with Positive Curvature

In this paper, we obtain some topological characterizations for the warping function of a warped product pointwise semi-slant submanifold of the form Omega(n) = N-T(l) x N-f(phi)k in a complex projective space CP2m (4). Additionally, we will find certain restrictions on the warping function f, Dirichlet energy function E(f), and first non-zero eigenvalue lambda(1) to prove that stable l-currents do not exist and also that the homology groups have vanished in Omega(n). As an application of the non-existence of the stable currents in Omega(n), we show that the fundamental group pi(1) (W-n) is trivial and Wn is simply connected under the same extrinsic conditions. Further, some similar conclusions are provided for CR-warped product submanifolds.