Riemannian Metrics on Locally Projectively Flat Manifolds
| dc.creator | Loftin, J. C. | |
| dc.date | 2001-08-30 | |
| dc.date.accessioned | 2026-07-07T04:43:12Z | |
| dc.date.available | 2026-07-07T04:43:12Z | |
| dc.description | The expression (-1/u) times the Hessian of u transforms as a symmetric (0,2) tensor under projective coordinate transformations, so long as u transforms as a section of a certain line bundle. On a locally projectively flat manifold M, the section u can be regarded as a metric potential analogous to the local potential in Kahler geometry. If M is compact and u is a negative section of the dual of the tautological bundle whose Hessian is positive definite, then M is projectively equivalent to a quotient of a bounded convex domain in R^n. The same is true if M has a boundary on which u=0. This theorem is analogous to a result of Schoen and Yau in locally conformally flat geometry. The proof uses affine differential geometry techniques developed by Cheng and Yau. | |
| dc.description | 16 pages, to be published in American Journal of Mathematics | |
| dc.identifier | https://arxiv.org/abs/math/0108218 | |
| dc.identifier | http://arxiv.org/abs/math/0108218 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62114 | |
| dc.subject | Differential Geometry | |
| dc.subject | 57N16 (Primary), 53A15 (Secondary) | |
| dc.title | Riemannian Metrics on Locally Projectively Flat Manifolds | |
| dc.type | text |