arXiv subjects

Rares Ambrosie

Publications and source records attributed to Rares Ambrosie.

2 recordsLinked to original sources

arXiv2025

New constructions of biharmonic polynomial maps between spheres

In this paper, we study diagonal maps between spheres given by two homogeneous polynomial maps between spheres, defined on the same domain sphere. First we find their bitension field, then we give a method for generating proper biharmonic maps between spheres, relying on harmonic homogeneous polynomial maps of different degrees. Further, we establish a result for constructing proper biharmonic product maps using harmonic homogeneous polynomial maps between spheres.

math.DG↗

arXiv2023

The energy density of biharmonic quadratic maps between spheres

In this paper, we first 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 $(m+1)/2$. Then, we give a positive answer to an open problem 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.

math.DG↗