This contributed volume includes chapters written by leading experts from around the world and provides a thorough and up-to-date exploration of geometric inequalities and their far-reaching applications. Covering a broad spectrum of topics, it discusses the intricacies of geometric solitons, generalized Ricci–Yamabe solitons on three-dimensional Lie groups, and Riemannian invariants in submanifold theory. Readers will find in-depth discussions on B.Y. Chen inequalities for submanifolds of Kenmotsu space forms, refined Chen–Ricci inequalities for submersions from Sasakian space forms, and essential characterizations of perfect fluid and generalized Robertson–Walker space-times admitting k-almost Ricci–Yamabe solitons. The book also investigates Riemannian concircular structure manifolds, statistical maps and their inequalities, as well as hyperbolic and η-hyperbolic Ricci–Yamabe solitons.