Some Classifications of Conformal Biharmonic and k-polyharmonic Maps
We give a complete classification of local and global conformal biharmonic maps between any two space forms by proving that a conformal map between two space forms is proper biharmonic if and only if the dimension is 4, the domain is flat, and it is a restriction of a Möbius transformation. We also...
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Veröffentlicht in: | Frontiers of Mathematics 2023, Vol.18 (1), p.1-15 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | We give a complete classification of local and global conformal biharmonic maps between any two space forms by proving that a conformal map between two space forms is proper biharmonic if and only if the dimension is 4, the domain is flat, and it is a restriction of a Möbius transformation. We also show that proper
k
-polyharmonic conformal maps between Euclidean spaces exist if and only if the dimension is 2
k
and they are precisely the restrictions of Möbius transformations. This provides infinitely many simple examples of proper
k
-polyharmonic maps with nice geometric structure. |
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ISSN: | 2731-8648 1673-3452 2731-8656 1673-3576 |
DOI: | 10.1007/s11464-021-0284-3 |