# Riemann curvature tensor on RCD spaces and possible applications

created by gigli on 06 Feb 2019

[BibTeX]

Preprint

Inserted: 6 feb 2019
Last Updated: 6 feb 2019

Year: 2019

Abstract:

We show that on every RCD spaces it is possible to introduce, by a distributional-like approach, a Riemann curvature tensor. Since after the works of Petrunin and Zhang-Zhu we know that finite dimensional Alexandrov spaces are RCD spaces, our construction applies in particular to the Alexan- drov setting. We conjecture that an RCD space is Alexandrov if and only if the sectional curvature - defined in terms of such abstract Riemann tensor - is bounded from below.