Riemannian Manifolds Admitting Isometric Immersions by Their First Eigenfunctions
نویسنده
چکیده
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 critical ones.
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تاریخ انتشار 2000