Conformal and semi-conformal biharmonic maps
We show that a conformal mapping between Riemannian manifolds of the same dimension n ≥ 3 is biharmonic if and only if the gradient of its dilation satisfies a certain second-order elliptic partial differential equation. On an Einstein manifold solutions can be generated from isoparametric function...
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| Veröffentlicht in: | Annals of global analysis and geometry 2008-11, Vol.34 (4), p.403-414 |
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| container_title | Annals of global analysis and geometry |
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| creator | Baird, Paul Fardoun, Ali Ouakkas, Seddik |
| description | We show that a conformal mapping between Riemannian manifolds of the same dimension
n
≥ 3 is biharmonic if and only if the gradient of its dilation satisfies a certain second-order elliptic partial differential equation. On an Einstein manifold solutions can be generated from isoparametric functions. We characterise those semi-conformal submersions that are biharmonic in terms of their dilation and the fibre mean curvature vector field. |
| doi_str_mv | 10.1007/s10455-008-9118-8 |
| format | Article |
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n
≥ 3 is biharmonic if and only if the gradient of its dilation satisfies a certain second-order elliptic partial differential equation. On an Einstein manifold solutions can be generated from isoparametric functions. We characterise those semi-conformal submersions that are biharmonic in terms of their dilation and the fibre mean curvature vector field.</description><identifier>ISSN: 0232-704X</identifier><identifier>EISSN: 1572-9060</identifier><identifier>DOI: 10.1007/s10455-008-9118-8</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Analysis ; Differential Geometry ; Euclidean space ; Geometry ; Global Analysis and Analysis on Manifolds ; Harmonic analysis ; Mapping ; Mathematical Physics ; Mathematics ; Mathematics and Statistics ; Original Paper ; Partial differential equations ; Studies</subject><ispartof>Annals of global analysis and geometry, 2008-11, Vol.34 (4), p.403-414</ispartof><rights>Springer Science+Business Media B.V. 2008</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c347t-1400c0675172066b96814db3d5bfb882508a0e3c2d6af2b844c32bd9df5845183</citedby><cites>FETCH-LOGICAL-c347t-1400c0675172066b96814db3d5bfb882508a0e3c2d6af2b844c32bd9df5845183</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10455-008-9118-8$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10455-008-9118-8$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27922,27923,41486,42555,51317</link.rule.ids></links><search><creatorcontrib>Baird, Paul</creatorcontrib><creatorcontrib>Fardoun, Ali</creatorcontrib><creatorcontrib>Ouakkas, Seddik</creatorcontrib><title>Conformal and semi-conformal biharmonic maps</title><title>Annals of global analysis and geometry</title><addtitle>Ann Glob Anal Geom</addtitle><description>We show that a conformal mapping between Riemannian manifolds of the same dimension
n
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| subjects | Analysis Differential Geometry Euclidean space Geometry Global Analysis and Analysis on Manifolds Harmonic analysis Mapping Mathematical Physics Mathematics Mathematics and Statistics Original Paper Partial differential equations Studies |
| title | Conformal and semi-conformal biharmonic maps |
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