An integral formula for a class of biharmonic maps from Euclidean 3-space (Q1654207)

The authors discuss semi-conformal maps from one Riemannian manifold \(\mathcal{M}=(M,g)\) to another Riemannian manifold \(\mathcal{N}=(N,h)\) and classify all semi-conformal biharmonic maps which are defined on an open subset of \(\mathbb{R}^3\) taking values in \(\mathbb{C}\) whose fibers are arcs of circles using holomorphic data. They give an integral formula for a class of biharmonic non-semi-conformal maps defined on open subsets of \(\mathbb{R}^3\).