Ricci curvature and Yamabe constants
| dc.creator | Petean, Jimmy | |
| dc.date | 2005-10-14 | |
| dc.date | 2005-10-30 | |
| dc.date.accessioned | 2026-07-07T06:47:30Z | |
| dc.date.available | 2026-07-07T06:47:30Z | |
| dc.description | We prove that if a closed unit volume Riemannian manifold, $(M^n, g)$, has Ricci curvature bounded from below by r>0 then the Yamabe constant of the conformal class of $g$ is at least $n.r$. This inequality has already been proved by S. Ilias (Constantes explicites pour les inegalites de Sobolev sur les varietes riemannienes compactes, Ann. Inst. Fourier 33, 151-165). The equality is achieved if the metric is Einstein (with Ricci curvature r). This implies for instance that if $h$ is the Fubini-Study metric on $CP^2$ and $g$ is any other metric on $CP^2$ with $Ricci(g) \geq Ricci(h)$ then $Vol(CP^2, g) \leq Vol(CP^2, h)$. | |
| dc.description | The author was informed that the inequality in the main theorem has already been proved by S. Ilias in Constantes explicites pour les inegalites de Sobolev sur les varietes riemanniennes compactes, Ann. Inst. Fourier 33, 151-165 | |
| dc.identifier | https://arxiv.org/abs/math/0510308 | |
| dc.identifier | http://arxiv.org/abs/math/0510308 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103672 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C21 | |
| dc.title | Ricci curvature and Yamabe constants | |
| dc.type | text |