SO(n)-invariant special Lagrangian submanifolds of C^{n+1} with fixed loci
| dc.creator | Bryant, Robert L. | |
| dc.date | 2004-02-12 | |
| dc.date | 2004-03-25 | |
| dc.date.accessioned | 2026-07-07T08:51:40Z | |
| dc.date.available | 2026-07-07T08:51:40Z | |
| dc.description | Let SO(n) act in the standard way on C^n and extend this action in the usual way to C^{n+1}. It is shown that a nonsingular special Lagrangian submanifold L in C^{n+1} that is invariant under this SO(n)-action intersects the fixed line C in a nonsingular real-analytic arc A (that may be empty). If n>2, then A has no compact component. Conversely, an embedded, noncompact nonsingular real-analytic arc A in C lies in an embedded nonsingular special Lagrangian submanifold that is SO(n)-invariant. The same existence result holds for compact A if n=2. If A is connected, there exist n distinct nonsingular SO(n)-invariant special Lagrangian extensions of A such that any embedded nonsingular SO(n)-invariant special Lagrangian extension of A agrees with one of these n extensions in some open neighborhood of A. The method employed is an analysis of a singular nonlinear PDE and ultimately calls on the work of Gerard and Tahara to prove the existence of the extension. | |
| dc.description | 19 pages, no figures. Miinor update: some misprints fixed and a reference added | |
| dc.identifier | https://arxiv.org/abs/math/0402201 | |
| dc.identifier | http://arxiv.org/abs/math/0402201 | |
| dc.identifier | Chinese Annals of Mathematics, Series B, vol. 27 no. 1 (January, 2006), pp. 95--112. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145012 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C42; 35A20 | |
| dc.title | SO(n)-invariant special Lagrangian submanifolds of C^{n+1} with fixed loci | |
| dc.type | text |