Proper biharmonic maps and $$(2,1)$$-harmonic morphisms from some wild geometries

Author:

Ghandour Elsa,Gudmundsson SigmundurORCID

Abstract

AbstractIn this work we construct a variety of new complex-valued proper biharmonic maps and (2, 1)-harmonic morphisms on Riemannian manifolds with non-trivial geometry. These are solutions to a non-linear system of partial differential equations depending on the geometric data of the manifolds involved.

Funder

Lund University

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Reference6 articles.

1. Baird, P., Wood, J.C.: Harmonic morphisms between Riemannian manifolds, The London Mathematical Society Monographs 29. Oxford University Press, UK (2003)

2. Fuglede, B.: Harmonic morphisms between Riemannian manifolds. Ann. Inst. Fourier 28, 107–144 (1978)

3. Ghandour, E., Gudmundsson, S.: Complex-valued $$(p,q)$$-harmonic morphisms from Riemannian manifolds, preprint (2020)

4. Ghandour, E., Ou, Y.-L.: Generalised harmonic morphisms and horizontally weakly conformal biharmonic maps. J. Math. Anal. Appl. 464, 924–938 (2018)

5. Gudmundsson, S.: The Bibliography of Harmonic Morphisms, www.matematik.lu.se/matematiklu/personal/sigma/harmonic/bibliography.html

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