Examples of Curvature Inhomogeneous Submanifolds with Constant Ricci Eigenvalues

Abstract

We construct two families of curvature inhomogeneous Riemannian manifolds with constant Ricci eigenvalues. The first, derived from the Einstein warped products, has two distinct Ricci eigenvalues and admits a local isometric immersion of minimum codimension two. The second, arising from the Riemannian Schwarzschild--Tangherlini manifold, has $k+1$ distinct Ricci eigenvalues and admits an isometric embedding of codimension $k+2$, which is the smallest within the adapted product class.