𝐿^{𝑝} almost conformal isometries of Sub-Semi-Riemannian metrics and solvability of a Ricci equation

Delay, Erwann

doi:10.1090/proc/13898

$L^p$ almost conformal isometries of Sub-Semi-Riemannian metrics and solvability of a Ricci equation
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Proc. Amer. Math. Soc. 146 (2018), 3499-3507 Request permission

Abstract:

Let $M$ be a smooth compact manifold without boundary. We consider two smooth Sub-Semi-Riemannian metrics on $M$. Under suitable conditions, we show that they are almost conformally isometric in an $L^p$ sense. Assume also that $M$ carries a Riemannian metric with parallel Ricci curvature. Then an equation of Ricci type is solvable in a specific sense, without assuming any proximity to a special metric.

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