English

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

Differential Geometry 2017-05-24 v1

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.

Keywords

Cite

@article{arxiv.1705.08352,
  title  = {A natural linear equation in affine geometry: the affine quasi-Einstein equation},
  author = {Miguel Brozos Vázquez and Eduardo García Río and Peter Gilkey and Xabier Valle Regueiro},
  journal= {arXiv preprint arXiv:1705.08352},
  year   = {2017}
}