Osserman manifolds of dimension 8
| dc.creator | Nikolayevsky, Y. | |
| dc.date | 2003-10-24 | |
| dc.date.accessioned | 2026-07-07T05:02:13Z | |
| dc.date.available | 2026-07-07T05:02:13Z | |
| dc.description | For a Riemannian manifold $M^n$ with the curvature tensor $R$, the Jacobi operator $R_X$ is defined by $R_XY = R(X,Y)X$. The manifold $M^n$ is called {\it pointwise Osserman} if, for every $p \in M^n$, the eigenvalues of the Jacobi operator $R_X$ do not depend of a unit vector $X \in T_pM^n$, and is called {\it globally Osserman} if they do not depend of the point $p$ either. R. Osserman conjectured that globally Osserman manifolds are flat or rank-one symmetric. This Conjecture is true for manifolds of dimension $n \ne 8, 16$. Here we prove the Osserman Conjecture and its pointwise version for 8-dimensional manifolds. | |
| dc.description | 18 pages, LaTEX | |
| dc.identifier | https://arxiv.org/abs/math/0310387 | |
| dc.identifier | http://arxiv.org/abs/math/0310387 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68973 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53B20, 53C25 | |
| dc.title | Osserman manifolds of dimension 8 | |
| dc.type | text |