A sufficient condition for the height function to be constant in $I_g{\times }_{\rho }{\mathbb{P}}^n$

This paper makes some modifications to the warped product space. Based on Alias,Impera and Rigoli, a warping function is added to the warped product space. This new function affects the Riemannian metric of the warped product space. In this new warped product space, we continue to discuss the sufficient condition for calculating the height of the immersed surface.