Lie Groups and Representation Theory

Seminar information archive ~06/14Next seminarFuture seminars 06/15~

Date, time & place Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.)


16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Jun-ichi Mukuno (Nagoya University)
Properly discontinuous isometric group actions on inhomogeneous Lorentzian manifolds (JAPANESE)
[ Abstract ]
If a homogeneous space $G/H$ is acted properly discontinuously
upon by a subgroup $\\Gamma$ of $G$ via the left action, the quotient space $\\Gamma \\backslash G/H$ is called a
Clifford--Klein form. In 1962, E. Calabi and L. Markus proved that there is no infinite subgroup of the Lorentz group $O(n+1, 1)$ whose left action on the de Sitter space $O(n+1, 1)/O(n, 1)$ is properly discontinuous.
It follows that a compact Clifford--Klein form of the de Sitter space never exists.
In this talk, we present a new extension of the theorem of E. Calabi and L. Markus to a certain class of Lorentzian manifolds that are not necessarily homogeneous.