We provide optimal pinching results on closed Einstein manifolds with positive Yamabe invariant in any dimension, extending the optimal bound for the scalar curvature due to Gursky and LeBrun in dimension four. We also improve the known bounds of the Yamabe invariant via the Ln2-norm of the Weyl tensor for low-dimensional Einstein manifolds. Finally, we discuss some advances on an algebraic inequality involving the Weyl tensor for dimensions 5 and 6.
Rigidity of Einstein manifolds with positive Yamabe invariant / L. Branca, G. Catino, D. Dameno, P. Mastrolia. - In: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY. - ISSN 0232-704X. - 67:4(2025), pp. 21.1-21.22. [Epub ahead of print] [10.1007/s10455-025-09996-x]
Rigidity of Einstein manifolds with positive Yamabe invariant
L. BrancaPrimo
;D. DamenoPenultimo
;P. Mastrolia
Ultimo
2025
Abstract
We provide optimal pinching results on closed Einstein manifolds with positive Yamabe invariant in any dimension, extending the optimal bound for the scalar curvature due to Gursky and LeBrun in dimension four. We also improve the known bounds of the Yamabe invariant via the Ln2-norm of the Weyl tensor for low-dimensional Einstein manifolds. Finally, we discuss some advances on an algebraic inequality involving the Weyl tensor for dimensions 5 and 6.
| File | Dimensione | Formato | |
|---|---|---|---|
|
unpaywall-bitstream-1929959803.pdf
accesso aperto
Tipologia:
Publisher's version/PDF
Licenza:
Creative commons
Dimensione
468.23 kB
Formato
Adobe PDF
|
468.23 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
