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

2017/05/23 by Vázquez, Miguel Brozos, Río, Eduardo García, Gilkey, Peter +1
#53B30 #53C21 #53C24 #53C44 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.08352

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.

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