Conformal and semi-conformal biharmonic maps (Q960014)

The authors show that a conformal mapping between equidimensional Riemannian manifolds of dimension \( n \geqq 3 \) is biharmonic iff the gradient of its dilatations satisfies a certain second-order elliptic partial differential equation. The authors first of all give two basic examples and then they characterise semi-conformal submersions that are biharmonic in terms of their dilatation and the fibre mean curvature vector field.