A Generalisation of Obata's theorem
| dc.creator | Ranjan, Akhil | |
| dc.creator | Santhanam, G. | |
| dc.date | 1995-11-23 | |
| dc.date.accessioned | 2026-07-07T09:12:38Z | |
| dc.date.available | 2026-07-07T09:12:38Z | |
| dc.description | In a complete Riemannian manifold $(M, g)$ if the hessian of a real valued function satisfies some suitable conditions then it restricts the geometry of $(M, g)$. In this paper we characterize all compact rank-1 symmetric spaces, as those Riemannian manifolds $(M, g)$ admitting a real valued function $u$ such that the hessian of $u$ has atmost two eigenvalues $-u$ and $-{{u+1}\over 2}$, under some mild hypothesis on $(M, g)$. This generalises a well known result of Obata which characterizes all round spheres. | |
| dc.description | 20 pages, uses Latex | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9511010 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9511010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152087 | |
| dc.subject | Differential Geometry | |
| dc.title | A Generalisation of Obata's theorem | |
| dc.type | text |