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We construct polynomial conformal invariants, the vanishing of which is necessary and sufficient for an $n$-dimensional suitably generic (pseudo-)Riemannian manifold to be conformal to an Einstein… (More)

- Daniel An, Pawel Nurowski
- 2014

On a natural circle bundle $${\mathbb{T}(M)}$$T(M) over a 4-dimensional manifold M equipped with a split signature metric g, whose fibers are real totally null selfdual 2-planes, we consider a… (More)

- Pawel Nurowski
- 1998

We define a certain differential system on an open set of R6. The system locally defines a Lorentzian four-manifold satisfying the Einstein equations. The converse statement is indicated and its… (More)

We explore and show a natural relationship between all third-order ordinary differential equations that possess a vanishing Wunschmann invariant, with conformal metrics on 3-manifolds and Cartan's… (More)

We provide an explicit formula for the Fefferman-Graham ambient metric of an n-dimensional conformal pp-wave in those cases where it exists. In even dimensions we calculate the obstruction… (More)

- Pawel Nurowski
- 2008

Abstract We provide the first examples of vacuum metrics with cosmological constant which have a twisting quadruple principal null direction.

We consider the nonstandard inclusion of SO(3) in SO(5) associated with a 5-dimensional irreducible representation. The tensor $\Upsilon$ representing this reduction is found to be given by a ternary… (More)

We prove several theorems concerning the connection between the local CR embeddability of 3-dimensional CR manifolds, and the existence of algebraically special Maxwell and gravitational fields. We… (More)

We present three large classes of examples of conformal structures for which the equations for the Fefferman-Graham ambient metric to be Ricci-flat are linear PDEs, which we solve explicitly. These… (More)

- Pawel Nurowski
- 1998

Given a conformally nonflat Einstein space–time we define a fibration P over it. The fibers of this fibration are elliptic curves (two-dimensional tori) or their degenerate counterparts. Their… (More)