5-dimensional geometries II: the non-fibered geometries

2016/05/24 by Andrew Geng, Geng, Andrew
Engineering · Mathematics · #Structural Analysis and Optimization #Geometric and Algebraic Topology #Elasticity and Material Modeling

paper · pdf · doi:10.48550/arxiv.1605.07534

Abstract

We classify the 5-dimensional homogeneous geometries in the sense of Thurston. The present paper (part 2 of 3) classifies those in which the linear isotropy representation is either irreducible or trivial. The 5-dimensional geometries with irreducible isotropy are the irreducible Riemannian symmetric spaces, while those with trivial isotropy are simply-connected solvable Lie groups of the form ℝ³ \rtimes ℝ² or N \rtimes ℝ where N is nilpotent.

Related

• 5-dimensional geometries III: the fibered geometries
• 5-dimensional geometries I: the general classification
• A classification of Thurston geometries without compact quotients
• Finite homogeneous geometries
• Special Riemannian geometries modeled on distinguished symmetric spaces