Characterizing Base in Warped Product Submanifolds of Complex Projective Spaces by Differential Equations

Abstract

In this study, a link between the squared norm of the second fundamental form and the Laplacian of the warping function for a warped product pointwise semi-slant submanifold Mn in a complex projective space is presented. Some characterizations of the base NT of Mn are offered as applications. We also look at whether the base NT is isometric to the Euclidean space Rp or the Euclidean sphere Sp, subject to some constraints on the second fundamental form and warping function.

Keywords

• warped products
• complex projective spaces
• Dirichlet energy
• Ricci curvature
• ordinary differential equations