A natural linear equation in affine geometry: The affine quasi-Einstein Equation

Brozos-Vázquez, Miguel; García-Río, Eduardo; Gilkey, Peter; Valle-Regueiro, Xabier

doi:10.1090/proc/14090

A natural linear equation in affine geometry: The affine quasi-Einstein Equation
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by Miguel Brozos-Vázquez, Eduardo García-Río, Peter Gilkey and Xabier Valle-Regueiro PDF

Proc. Amer. Math. Soc. 146 (2018), 3485-3497 Request permission

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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