The topological obstructions to the existence of an irreducible SO(3) structure on a five manifold

2006/01/04 by Marcin Bobieński, Bobienski, Marcin
Computer Science · Mathematics · #53C10 #53C15 #57R15 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.math/0601066

openalex publication_date 2006/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A nonstandard (maximal) inclusion SO(3) in SO(5) associated with the irreducible representation ρ₅ of SO(3) in R⁵ is considered. The topological obstructions for admitting the SO(3) structure on the frame bundle over 5-manifold are investigated. The necessary and sufficient conditions are formulated.

Citations

• On types of non-integrable geometries

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