Harmonic manifolds with some specific volume densities
| dc.creator | Ramachandran, K. | |
| dc.creator | Ranjan, Akhil | |
| dc.date | 1996-03-24 | |
| dc.date.accessioned | 2026-07-07T09:12:44Z | |
| dc.date.available | 2026-07-07T09:12:44Z | |
| dc.description | We show that noncompact simply connected harmonic manifolds with volume density $Θ_{p}(r) =\sinh ^{n-1} r$ is isometric to the real hyperbolic space and noncompact simply connected Kähler harmonic manifold with volume density $Θ_{p}(r) =\sinh ^{2n-1} r \cosh r$ is isometric to the complex hyperbolic space. A similar result is also proved for Quaternionic Kähler manifolds. Using our methods we get an alternative proof, without appealing to the powerful Cheeger-Gromoll splitting theorem, of the fact that every Ricci flat harmonic manifold is isometric to the euclidean space. Finally a rigidity result for real hyperbolic space is presented. | |
| dc.description | 10 pages, latex (e-mail: kram@..., aranjan@ganit.math.iitb.ernet.in) | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9603013 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9603013 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152122 | |
| dc.subject | Differential Geometry | |
| dc.title | Harmonic manifolds with some specific volume densities | |
| dc.type | text |