Willmore Legendrian surfaces in pseudoconformal 5-sphere
| dc.creator | Wang, Sung Ho | |
| dc.date | 2007-07-03 | |
| dc.date.accessioned | 2026-07-07T08:13:43Z | |
| dc.date.available | 2026-07-07T08:13:43Z | |
| dc.description | Let $ X: M \hook S^5$ be a compact Legendrian surface in pseudoconformal(CR) 5-sphere. We introduce a pseudoconformally invariant Willmore type second order functional $ \W(X)$, and study its critical points called Willmore Legendrian surfaces. The fifth order structure equations show that Willmore dual can be defined for a class of Willmore Legendrian surfaces. Moreover when this dual is constant, Willmore Legendrian surface admits a Weierstraßtype representation in terms of immersed meromorphic curve in $ \C^2$ satisfying an appropriate real period condition via pseudoconformal stereographic projection. We show that every compact Riemann surface admits a generally one to one, conformal, Willmore Legendrian immersion in $ S^5$ with constant Willmore dual. As a corollary, every compact Riemann surface can be conformally immersed in $ \C^2$ as an exact, algebraic Lagrangian surface. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/0707.0366 | |
| dc.identifier | http://arxiv.org/abs/0707.0366 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132869 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 53D12, 53A07 | |
| dc.title | Willmore Legendrian surfaces in pseudoconformal 5-sphere | |
| dc.type | text |