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

## TL;DR

This paper investigates conditions under which two Sub-Semi-Riemannian metrics on a compact manifold are approximately conformally isometric in an Lp sense and explores the solvability of a Ricci-type equation without proximity assumptions.

## Contribution

It establishes almost conformal isometries between Sub-Semi-Riemannian metrics and demonstrates Ricci equation solvability under broad conditions, extending previous results.

## Key findings

- Metrics are almost conformally isometric in Lp sense under certain conditions
- Ricci-type equation is solvable without closeness assumptions
- Results apply to manifolds with parallel Ricci curvature

## 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 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.