2016/05/24 by Geng, Andrew
#53C30 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1605.07546
We classify the 5-dimensional homogeneous geometries in the sense of Thurston. The present paper (part 3 of 3) classifies those in which the linear isotropy representation is nontrivial but reducible. Most of the resulting geometries are products. Some interesting examples include a countably infinite family of inequivalent geometries diffeomorphic to S3 × S2; an uncountable family in which only a countable subfamily admits compact quotients; and the non-maximal geometry SO(4)/SO(2) realized by two distinct maximal geometries.