Hi,
Let $\varphi$ be an isometry of a simply connected pseudo Riemannian manifold $M$. The squared displacement function of $\varphi$ is $d^2_{\varphi}(p):=d^2(\varphi (p),p)$, $p\in M$, where $d$ is the distance on $M$. By a theorem of J.A.Wolf, if $M$ is complete Riemannian manifold of negative sectional curvature then $\varphi$ is the identity iff $d^2_{\varphi}$ is constant (and $d^2_{\varphi}$ is constant iff it is bounded).
Now, my question is that if $\varphi$ is an isometry of a Lorentzian space form (specially $\widetilde{AdS}_n$, the universal covering of the anti de Sitter space) is there any sufficient condition under which one can deduce that $\varphi$ is the identity?
Thanks.
Take the 2minute tour
×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.


