Combinatorics

Image warping

Topology (electrical circuits)

Pure mathematics

Mathematics

Submanifold

Mathematical analysis

Artificial intelligence

Curvature

Geometry

Pointwise

Computer science

Product (mathematics)

In this paper, we obtain some topological characterizations for the warping function of a warped product pointwise semi-slant submanifold of the form Ωn=NTl×fNϕk 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 λ1 to prove that stable l-currents do not exist and also that the homology groups have vanished in Ωn. As an application of the non-existence of the stable currents in Ωn, we show that the fundamental group π1(Ωn) is trivial and Ωn is simply connected under the same extrinsic conditions. Further, some similar conclusions are provided for CR-warped product submanifolds.

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