Refine search
Actions for selected content:
1 results
Conformally Kähler structures
- Part of
-
- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View
- Published online by Cambridge University Press:
- 11 August 2025, pp. 1-17
-
- Article
-
- You have access
- Open access
- HTML
- Export citation
-
We establish a one-to-one correspondence between Kähler metrics in a given conformal class and parallel sections of a certain vector bundle with conformally invariant connection, where the parallel sections satisfy a set of non-linear algebraic constraints that we describe. The vector bundle captures 2-form prolongations and is isomorphic to
$\Lambda^3(\mathcal{T})$, where 
${\mathcal{T}}$ is the tractor bundle of conformal geometry, but the resulting connection differs from the normal tractor connection by curvature terms.Our analysis leads to a set of obstructions for a Riemannian metric to be conformal to a Kähler metric. In particular, we find an explicit algebraic condition for a Weyl tensor which must hold if there exists a conformal Killing–Yano tensor, which is a necessary condition for a metric to be conformal to Kähler. This gives an invariant characterization of algebraically special Riemannian metrics of type D in dimensions higher than four.
