Optimal inequalities for submanifolds of Riemann manifolds of nearly quasi-constant curvature with quarter-symmetric connection

Abstract

In this paper, we obtain Chen inequalities for submanifolds in Riemannian manifolds of nearly quasi-constant curvature with a special kind of quartersymmetric connection and discuss the equality case of the inequalities. We also obtain some Casorati inequalities for submanifolds in Riemannian manifolds of nearly quasi-constant curvature with the quarter-symmetric connection.