On pseudometrics for generalized uniform structures

Abstract

Proof.If M is Ricci flat it is trivially Einstein and, since L2 -HL = 0, one of the principal curvatures is zero.If R* = bl, then L2-HL + bI = 0.If K = 0, then there is a zero principal curvature and a unit principal vector X with LX = 0. Hence bX = 0soR* = 0.In the case « = 3, the characteristic polynomial L% -HL2 + JL -KI = 0 implies JL = 0, and since Lm = 0 implies J(m) = 0, we have J=0.

Locations

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