Abstract
The study follows the conjecture of Lawson and Simon (1973) and proves the main theorems. If the warping function of a compact warped product Lagrangian submanifold Sigma(3) isometrically immersed into the nearly Kaehler 6-sphere, satisfies several extrinsic conditions, then there are no stable integral currents in Sigma(3) and homology groups are vanished in Sigma(3). As applications, we show that Sigma(3) is homotopic to a sphere S-3 and fundamental group or first homotopy group pi(1)(Sigma(3)) is vanished under the same restrictions. Finally, we discuss some related results as well. (C) 2020 Elsevier B.V. All rights reserved.