Lp almost conformal isometries of Sub-Semi-Riemannian metrics and solvability of a Ricci equation

Erwann Delay (1)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon

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 Lp sense. Assume also that M carries a Riemannian metric with parallel Ricci curvature. Then an equation of Ricci type, is in some sense solvable, without assuming any closeness near a special metric.

Keywords: Einstein metrics; Sub-Semi-Riemannian metrics; Ricci curvature; Inverse problem; Quasilinear elliptic systems

Domains: Mathematics [math]; Differential Geometry [math.DG]

Erwann Delay. Lp almost conformal isometries of Sub-Semi-Riemannian metrics and solvability of a Ricci equation. 2017. ⟨hal-01440190⟩