Estimation of sharp geometric inequality in \(D_{\alpha}\)-homothetically deformed Kenmotsu manifolds

Abstract

In this article, we investigate the Kenmotsu manifold when applied to a \(D_{\alpha}\)-homothetic deformation. Then, given a submanifold in a \(D_{\alpha}\)-homothetically deformed Kenmotsu manifold, we derive the generalized Wintgen inequality. Additionally, we find this inequality for submanifolds such as slant, invariant, and anti-invariant in the same ambient space.

Keywords

• normalized scalar curvature
• scalar curvature
• mean curvature
• dα-homothetic deformation