Let R be an algebraic curvature tensor for a non-degenerate inner product of signature (p, q) where q ≥ 5. If π is a spacelike 2 plane, let R(π) be the associated skewsymmetric curvature operator. We classify the algebraic curvature tensors so R(·) has constant rank 2 and show these are geometrically realizable by hypersurfaces in flat spaces. We also classify the Ivanov-Petrova algebraic curva...

This article presents a new definition of Branson’s Q-curvature in even dimensional conformal geometry. The Q-curvature is a generalization of the scalar curvature in dimension 2: it satisfies an analogous transformation law under conformal rescalings of the metric and on conformally flat manifolds its integral is a multiple of the Euler characteristic. Our approach is motivated by the recent w...

Over forty years ago, Paneitz, and independently Fradkin Tseytlin, discovered a fourth-order conformally-invariant differential operator, intrinsically defined on conformal manifold, mapping scalars to scalars. This operator is special case of the so-termed extrinsic Paneitz in when manifold itself conformally embedded hypersurface. In particular, this encodes obstruction smoothly solving five-...