Riemannian manifolds admitting isometric immersions by their first eigenfunctions
Riemannian manifolds admitting isometric immersions by their first eigenfunctions
Given a compact manifold M, we prove that every critical Riemannian metric g for the functional "first eigenvalue of the Laplacian" is λ 1 -minimal (i.e., (M, g) can be immersed isometrically in a sphere by its first eigenfunctions) and give a sufficient condition for a λ 1 -minimal metric …