Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.09543 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908887446192128 |
|---|---|
| author | Ren, Guangzhen Tang, Kai Wu, Qingyan |
| author_facet | Ren, Guangzhen Tang, Kai Wu, Qingyan |
| contents | We introduce the notion of a rank-3 generalized Clifford manifold, defined by a triple of generalized complex structures satisfying Clifford-type relations. We show that every such structure canonically induces a generalized hypercomplex structure. We further describe a natural Spin(3)-action by Clifford rotations, which produces an $S^2 \times S^2$-family of generalized complex structures. The corresponding twistor space is then constructed, and we prove that the induced almost generalized complex structure is integrable. In contrast to the standard pure-spinor approach, the integrability of the twistor-space structure is established entirely in terms of the generalized Nijenhuis tensor. We further prove that this Clifford-to-twistor construction is compatible with T-duality, in the sense that T-duality preserves the rank-3 Clifford triple, the induced structures, and the associated Spin(3)-rotated family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09543 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | rank-3 generalized Clifford manifold and its twistor space Ren, Guangzhen Tang, Kai Wu, Qingyan Complex Variables We introduce the notion of a rank-3 generalized Clifford manifold, defined by a triple of generalized complex structures satisfying Clifford-type relations. We show that every such structure canonically induces a generalized hypercomplex structure. We further describe a natural Spin(3)-action by Clifford rotations, which produces an $S^2 \times S^2$-family of generalized complex structures. The corresponding twistor space is then constructed, and we prove that the induced almost generalized complex structure is integrable. In contrast to the standard pure-spinor approach, the integrability of the twistor-space structure is established entirely in terms of the generalized Nijenhuis tensor. We further prove that this Clifford-to-twistor construction is compatible with T-duality, in the sense that T-duality preserves the rank-3 Clifford triple, the induced structures, and the associated Spin(3)-rotated family. |
| title | rank-3 generalized Clifford manifold and its twistor space |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2603.09543 |