Convergence to the Product of the Standard Spheres and Eigenvalues of the Laplacian

Abstract

We show a Gromov-Hausdorff approximation to the product of the standard spheres 𝑆ⁿ⁻ᵖ × 𝑆ᵖ for Riemannian manifolds with positive Ricci curvature under some pinching condition on the eigenvalues of the Laplacian acting on functions and forms.