Affine connections with W=0
| dc.creator | Burstall, Francis | |
| dc.creator | Rawnsley, John | |
| dc.date | 2007-02-01 | |
| dc.date | 2007-02-26 | |
| dc.date.accessioned | 2026-07-07T07:48:28Z | |
| dc.date.available | 2026-07-07T07:48:28Z | |
| dc.description | For a torsionless connection on the tangent bundle of a manifold M the Weyl curvature W is the part of the curvature in kernel of the Ricci contraction. We give a coordinate free proof of Weyl's result that the Weyl curvature vanishes if and only if the manifold is (locally) diffeomorphic to a real projective space with the connection, when transported to the projective space, in the projective class of the Levi-Civita connection of the Fubini-Study metric. Associated to a connection on an even-dimensional M is an almost complex structure on J(M) the bundle of all complex structures on the tangent spaces of M, c.f. [O'Brian-Rawnsley]. We show that this structure is a projective invariant, and when integrable can be obtained from a torsionless connection which must then have W=0. We also show that two torsionless connections define the same almost complex structure if and only if they are projectively equivalent. | |
| dc.description | 18 pages. Revised bibliography | |
| dc.identifier | https://arxiv.org/abs/math/0702032 | |
| dc.identifier | http://arxiv.org/abs/math/0702032 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124512 | |
| dc.subject | Differential Geometry | |
| dc.title | Affine connections with W=0 | |
| dc.type | text |