We show that, on every RCD space, 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 Alexandrov 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.
Riemann curvature tensor on RCD spaces and possible applications / Gigli, N.. - In: COMPTES RENDUS MATHÉMATIQUE. - ISSN 1631-073X. - 357:7(2019), pp. 613-619. [10.1016/j.crma.2019.06.003]
Riemann curvature tensor on RCD spaces and possible applications
Gigli, N.
2019-01-01
Abstract
We show that, on every RCD space, 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 Alexandrov 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.| File | Dimensione | Formato | |
|---|---|---|---|
|
Sectional-rev.pdf
accesso aperto
Tipologia:
Documento in Post-print
Licenza:
Non specificato
Dimensione
282.79 kB
Formato
Adobe PDF
|
282.79 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
