A natural linear equation in affine geometry: the affine quasi-Einstein equation

Abstract

We study the affine quasi-Einstein equation, a second order linear homogeneous equation, which is invariantly defined on any affine manifold. We prove that the space of solutions is finite-dimensional, and its dimension is a strongly projective invariant. Moreover the maximal dimension is shown to be achieved if and only if the manifold is strongly projectively flat.

References in corpus (3)

• Homogeneous affine surfaces: affine Killing vector fields and Gradient Ricci solitons
• Half conformally flat generalized quasi-Einstein manifolds
• Moduli spaces of oriented Type A manifolds of dimension at least 3

Cited by in corpus (2)

• Applications of PDEs to the study of affine surface geometry
• Solutions to the affine quasi-Einstein equation for homogeneous surfaces