Horizontality with infinite complexity in the twistor spaces on tori

2024/02/05 by Naoya Ando, Ando, Naoya, Anri Yonezaki +1 · 1 citation
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2402.02748

openalex publication_date 2024/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the complexity of horizontality in the twistor space E associated with an oriented vector bundle E of rank 4 with a positive-definite metric over a torus. If the horizontality has finite complexity of degree d>2 for an element of a fiber of E, then the complexity is expressed in terms of a finite subgroup of SO(3) ([3]). In the present paper, we observe that if the horizontality has infinite complexity derived from one of the cases studied in [3], then the complexity is expressed by a dense subset of S².

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• Classification of the topological holonomy groups in SO(3)

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