On rigidity of Grauert tubes over homogeneous Riemannian manifolds
| dc.creator | Kan, Su-Jen | |
| dc.date | 2003-10-06 | |
| dc.date | 2004-03-10 | |
| dc.date.accessioned | 2026-07-07T05:01:39Z | |
| dc.date.available | 2026-07-07T05:01:39Z | |
| dc.description | Given a real-analytic Riemannian manifold $X$ there is a canonical complex structure, which is compatible with the canonical complex structure on $T^*X$ and makes the leaves of the Riemannian foliation on $TX$ into holomorphic curves, on its tangent bundle. A {\it Grauert tube} over $X$ of radius $r$, denoted as $T^rX$, is the collection of tangent vectors of $X$ of length less than $r$ equipped with this canonical complex structure. In this article, we prove the following two rigidity property of Grauert tubes. First, for any real-analytic Riemannian manifold such that $r_{max}>0$, we show that the identity component of the automorphism group of $T^rX$ is isomorphic to the identity component of the isometry group of $X$ provided that $r<r_{max}$. Secondly, let $X$ be a homogeneous Riemannian manifold and let the radius $r<r_{max}$, then the automorphism group of $T^rX$ is isomorphic to the isometry group of $X$ and there is a unique Grauert tube representation for such a complex manifold $T^rX$. | |
| dc.description | 23 pages. J.reine angew. Math. (to appear) | |
| dc.identifier | https://arxiv.org/abs/math/0310069 | |
| dc.identifier | http://arxiv.org/abs/math/0310069 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68752 | |
| dc.subject | Complex Variables | |
| dc.subject | 32C09;32Q28;32Q45 | |
| dc.title | On rigidity of Grauert tubes over homogeneous Riemannian manifolds | |
| dc.type | text |