A NATURAL LINEAR EQUATION IN AFFINE GEOMETRY: THE AFFINE QUASI-EINSTEIN EQUATION

作者：Brozos Vazquez Miguel^*; Garcia Rio Eduardo; Gilkey Peter; Valle Regueiro Xabier

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 146(8): 3485-3497.

DOI：10.1090/proc/14090

• Strong projective equivalence
• Liouville's equivalence
• projectively flat
• affine quasi-Einstein equation

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.

• 出版日期2018-8