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Conformal and semi-conformal biharmonic maps. (English) Zbl 1158.53049

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.
Reviewer: Jan Kurek (Lublin)

MSC:

53C43 Differential geometric aspects of harmonic maps
31B30 Biharmonic and polyharmonic equations and functions in higher dimensions
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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