Chen Inequalities for Submanifolds of Kenmotsu Space Forms

This chapter explores Chen-Ricci inequalities for submanifolds of Kenmotsu space forms endowed with a ϕ−η-connection, a special type of quarter-symmetric metric connection. The geometric background of Kenmotsu space forms and the properties of the ϕ−η-connection are briefly introduced, followed by the derivation of relevant curvature relations. The study proceeds by examining submanifolds within this framework, focusing on the behavior of curvature tensors and associated Riemannian invariants. Using the properties of the ambient space and the chosen connection, several inequalities involving Chen invariants and Ricci curvatures are obtained.