Department of Mathematics
Title : Local obstructions to 2-dimensional projective structures admitting skew-symmetric Ricci tensor
| Speaker: Matthew Randall Affiliation: Australian National University Time: 11:00 Tuesday, 2 August, 2011 Location: 439-G10 |
Abstract
| A projective surface is a 2-dimensional manifold equipped with a projective structure i.e. a class of torsion-free affine connections that have the same geodesics as unparameterised curves. Given any projective surface we can ask whether it admits a torsion-free affine connection (in its projective class) that has skew-symmetric Ricci tensor. This is equivalent to solving a particular semi-linear overdetermined partial differential equation that generalises the projectively Ricci-flat condition. It turns out that there are local obstructions to solving the PDEin two dimensions. These obstructions are constructed out of local invariants of the projective structure. |
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Programmes and Centres
- New Zealand Institute of Mathematics and its Applications (NZIMA)
- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
