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

We classify biharmonic semi-conformal maps from domains of Euclidean 3-space whose fibres are arcs of circles in terms of holomorphic data. The geometry behind this classification enables us to give an integral formula which produces biharmonic maps which are now no longer necessarily semi-conformal. An integral invariant for bounded singular sets of more general semi-conformal maps is obtained.