Abstract
For a given minimal Legendrian submanifold L of a Sasaki–Einstein manifold we construct two families of eigenfunctions of the Laplacian of L and we give a lower bound for the dimension of the corresponding eigenspace. Moreover, in the case the lower bound is attained, we prove that L is totally geodesic and a rigidity result about the ambient manifold. This is a generalization of a result for the standard Sasakian sphere done by Lê and Wang.
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