Riemannian Manifolds Admitting Isometric Immersions by Their First Eigenfunctions

@inproceedings{Soufi2000RiemannianMA,
  title={Riemannian Manifolds Admitting Isometric Immersions by Their First Eigenfunctions},
  author={Ahmad El Soufi and S{\"a}ıd Ilias},
  year={2000}
}
Given a compact manifold M, we prove that every critical Riemannian metric g for the functional “first eigenvalue of the Laplacian” is λ1-minimal (i.e., (M, g) can be immersed isometrically in a sphere by its first eigenfunctions) and give a sufficient condition for a λ1-minimal metric to be critical. In the second part, we consider the case where M is the 2dimensional torus and prove that the flat metrics corresponding to square and equilateral lattices of R are the only λ1minimal and the only… CONTINUE READING
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