Principal Distribution Isomorphisms and Almost Hermitian geometry on Isoparametric Hypersurfaces
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918327641702400 |
|---|---|
| author | Xiao, Lixin Yan, Wenjiao Zhang, Wenjin |
| author_facet | Xiao, Lixin Yan, Wenjiao Zhang, Wenjin |
| contents | This paper investigates the isomorphisms between principal distributions $\mathcal{D}_k$ $(k=1,\dots 4)$ on OT--FKM type isoparametric hypersurfaces in spheres. We recover the isomorphism $\mathcal{D}_1 \cong \mathcal{D}_3$ established by Qian--Tang--Yan \cite{Q-T-Y 2}, and further construct the isomorphism $\mathcal{D}_{2}\cong\mathcal{D}_{4}$ in specific cases. More significantly, we provide an explicit construction of a global vector bundle isomorphism $\mathcal{D}_1 \oplus \mathcal{D}_2 \cong \mathcal{D}_3 \oplus \mathcal{D}_4$ for all odd multiplicities $m$. As applications, we employ these isomorphisms to induce nearly Kähler structures on certain OT--FKM hypersurfaces. Finally, we prove that the $*$-Ricci curvature vanishes for any OT--FKM hypersurface admitting an almost Hermitian structure that interchanges principal distributions in pairs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08001 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Principal Distribution Isomorphisms and Almost Hermitian geometry on Isoparametric Hypersurfaces Xiao, Lixin Yan, Wenjiao Zhang, Wenjin Differential Geometry Complex Variables 53C15 (Primary) 32Q60, 58A30 (Secondary) This paper investigates the isomorphisms between principal distributions $\mathcal{D}_k$ $(k=1,\dots 4)$ on OT--FKM type isoparametric hypersurfaces in spheres. We recover the isomorphism $\mathcal{D}_1 \cong \mathcal{D}_3$ established by Qian--Tang--Yan \cite{Q-T-Y 2}, and further construct the isomorphism $\mathcal{D}_{2}\cong\mathcal{D}_{4}$ in specific cases. More significantly, we provide an explicit construction of a global vector bundle isomorphism $\mathcal{D}_1 \oplus \mathcal{D}_2 \cong \mathcal{D}_3 \oplus \mathcal{D}_4$ for all odd multiplicities $m$. As applications, we employ these isomorphisms to induce nearly Kähler structures on certain OT--FKM hypersurfaces. Finally, we prove that the $*$-Ricci curvature vanishes for any OT--FKM hypersurface admitting an almost Hermitian structure that interchanges principal distributions in pairs. |
| title | Principal Distribution Isomorphisms and Almost Hermitian geometry on Isoparametric Hypersurfaces |
| topic | Differential Geometry Complex Variables 53C15 (Primary) 32Q60, 58A30 (Secondary) |
| url | https://arxiv.org/abs/2602.08001 |