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arXiv · 1207.0128

Einstein metrics in projective geometry

A. Cap·A. R. Gover·H. R. Macbeth
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Abstract

It is well known that pseudo-Riemannian metrics in the projective class of a given torsion free affine connection can be obtained from (and are equivalent to) the solutions of a certain overdetermined projectively invariant differential equation. This equation is a special case of a so-called first BGG equation. The general theory of such equations singles out a subclass of so-called normal solutions. We prove that non-degerate normal solutions are equivalent to pseudo-Riemannian Einstein metrics in the projective class and observe that this connects to natural projective extensions of the Einstein condition.

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BibTeXRIS

A. Cap, A. R. Gover, H. R. Macbeth. 2012-06-30. Einstein metrics in projective geometry. https://doi.org/10.1007/s10711-013-9828-3

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