On the stochastically complete hypersurfaces in the product spaces M n ( κ ) x R

A Simons-type equation for hypersurfaces in a product space M-n(kappa) x R, where M-n(kappa) is a Riemannian manifold with constant sectional curvature kappa, is derived. Several applications are presented, including those for stochastically complete hypersurfaces with zero mean curvature and nonzero constant mean curvature in these spaces. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, Al training, and similar technologies.