Analysis of stable currents and homology of biwarped product submanifolds in the Euclidean space

Abstract

This paper examines the topological features of the compact biwarped product submanifolds of a space form with vanishing constant sectional curvature. More precisely, we show that stable integral p?current does not exist in a compact oriented biwarped product submanifold in an Euclidean space that meets some geometric conditions based on Laplacian of warping functions, slant functions. Simultaneously, it is shown that their homology group are zero under these geometric conditions. Additionally, some special cases are also described.