Naoya Ando

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math.DG2025

Classification of the topological holonomy groups in $S O (3)$

Naoya Ando

In this paper, we obtain classification of the topological holonomy groups in $S O (3)$ . Such a group is given by one of the following: a finite group (such groups are classified by…

math.DG2024

The topological holonomy group and the complexity of horizontality

Naoya Ando, Anri Yonezaki

Based on [1], we study the complexity of horizontality in each twistor space $E^_{ε}$ associated with an oriented vector bundle $E$ of rank $4$ with a positive-defin…

math.DG2024

Nilpotent structures of oriented neutral vector bundles

Naoya Ando

In this paper, we study nilpotent structures of an oriented vector bundle $E$ of rank $4 n$ with a neutral metric $h$ and an $h$ -connection $\nabla$ . We define $H$ -nilpotent structu…

math.DG2024

Horizontality with infinite complexity in the twistor spaces on tori

Naoya Ando, Anri Yonezaki

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 t…

math.DG2023

The $S O (3, 1)$ -orbits in the light cone of the 2-fold exterior power of the Minkowski 4-space

Naoya Ando

Two special neutral hypersurfaces $L_{\pm}$ in the light cone $L (⋀^{2} E_{1}^{4})$ studied in [1], [3] are $S O (3, 1)$ -orbits. In this paper, we see that each $S O (3, 1)$ -…

Classification of the topological holonomy groups in SO(3)

The topological holonomy group and the complexity of horizontality

Nilpotent structures of oriented neutral vector bundles

Horizontality with infinite complexity in the twistor spaces on tori

The SO(3,1)-orbits in the light cone of the 2-fold exterior power of the Minkowski 4-space

Classification of the topological holonomy groups in $S O (3)$

The $S O (3, 1)$ -orbits in the light cone of the 2-fold exterior power of the Minkowski 4-space