5 problems

Let $(\mathbb{R}^4,g)$ be a Ricci-flat pp-wave with metric … where $H\colon\mathbb{R}\times\mathbb{R}^2\to\mathbb{R}$. Ehlers–Kundt conjecture. The metric is geodesically complete…

Consider quadratic metric-affine gravity with a pp-metric and explicitly given purely axial torsion whose Ricci curvature is parallel. Purely axial torsion pp-wave conjecture. Ther…

Let $({\cal M},\mathrm{g})$ be an indecomposable locally homogeneous pp-wave of dimension greater than $3$. Let $V$ denote the parallel null vector field of the pp-wave, let…

Let $({\cal M},\mathrm{g})$ be an indecomposable locally homogeneous pp-wave of dimension greater than $3$. A locally homogeneous pp-wave is a pp-wave whose local Killing vector fi…

Let $(M,g)$ be a $pp$-wave, and let $P_{2k}$ denote its GJMS operators. Since the scalar curvature of a $pp$-wave vanishes, the Laplacian $44_g$ is conformally covariant; calculati…