Towards Kaluza-Klein Dark Matter on Nilmanifolds
  We present a first study of the field spectrum on a class of negatively-curved compact spaces: nilmanifolds or twisted tori. This is a case where analytical results can be obtained, allowing to check numerical methods. We focus on the Kaluza-Klein expansion of a scalar field. The results are then applied to a toy model where a natural Dark Matter candidate arises as a stable massive state of the bulk scalar. 
David Andriot, Giacomo Cacciapaglia, Aldo Deandrea, Nicolas   Deutschmann, Dimitrios Tsimpis
hep-th hep-ph math.SP