The energy density of biharmonic quadratic maps between spheres

In this paper, we first prove that a quadratic form from Sm to Sn is non-harmonic biharmonic if and only if it has constant energy density (m + 1)/2. Then, we give a positive answer to an open problem raised in [1] concerning the structure of non-harmonic biharmonic quadratic forms. As a direct application, using classification results for harmonic quadratic forms, we infer classification results for non-harmonic biharmonic quadratic forms. (c) 2023 Elsevier B.V. All rights reserved.