Rareş Ambrosie
Alexandru Ioan Cuza University, Iaşi, Romania

In this talk, we report on biharmonic quadratic maps between spheres. First, we prove a characterization formula for biharmonic maps in Euclidean spheres. Then, for the special case of maps between spheres whose components are given by homogeneous polynomials of the same degree, we find a more specific form for their bitension field. Further, we apply this formula to the case when the degree is $2$, and we prove that a quadratic form from $\mathbb{S}^m$ to $\mathbb{S}^n$ is non-harmonic biharmonic if and only if it has constant energy density $(m + 1)/2$. We end by presenting some classification results for biharmonic $q$-forms.