Classification of the topological holonomy groups in SO(3)

2025/07/28 by Ando, Naoya
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.20593

Abstract

In this paper, we obtain classification of the topological holonomy groups in SO(3). Such a group is given by one of the following: a finite group (such groups are classified by Klein); a commutative infinite group which is generated by one or two elements, and dense in a subgroup of SO(3) isomorphic to SO(2); a non-commutative infinite group generated by two elements of order 2, ∞ such that these rotation axes are orthogonal; a non-commutative infinite group which is dense in SO(3).

Citations

• Horizontality with infinite complexity in the twistor spaces on tori

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