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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2406.06753 |
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| _version_ | 1866908760306352128 |
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| author | Moreno, Andrés J. Portilla, Luis E. |
| author_facet | Moreno, Andrés J. Portilla, Luis E. |
| contents | We study homogeneous instantons on the seven dimensional Stiefel manifold V in the context of $G_2$ and Sasakian geometry. According to the reductive decomposition of V we provide an explicit description of all invariant $G_2$ and Sasakian structures. In particular, we characterise the invariant $G_2$- structures inducing a Sasakian metric, among which the well known nearly parallel $G_2$-structure (Sasaki- Einstein) is included. As a consequence, we classify the invariant connections on homogeneous principal bundles over V with gauge group U(1) and SO(3), satisfying either the $G_2$ or the Sasakian instanton condition. In addition, we study infinitesimal deformations of $G_2$-instantons on coclosed $G_2$-manifolds using a spinorial approach. By means of a Weitzenböck-type formula with torsion, we obtain curvature obstructions to the existence of non-trivial infinitesimal deformations and prove rigidity results for certain homogeneous $G_2$-instantons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06753 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homogeneous G2 and Sasakian instantons on the Stiefel 7-manifold Moreno, Andrés J. Portilla, Luis E. Differential Geometry We study homogeneous instantons on the seven dimensional Stiefel manifold V in the context of $G_2$ and Sasakian geometry. According to the reductive decomposition of V we provide an explicit description of all invariant $G_2$ and Sasakian structures. In particular, we characterise the invariant $G_2$- structures inducing a Sasakian metric, among which the well known nearly parallel $G_2$-structure (Sasaki- Einstein) is included. As a consequence, we classify the invariant connections on homogeneous principal bundles over V with gauge group U(1) and SO(3), satisfying either the $G_2$ or the Sasakian instanton condition. In addition, we study infinitesimal deformations of $G_2$-instantons on coclosed $G_2$-manifolds using a spinorial approach. By means of a Weitzenböck-type formula with torsion, we obtain curvature obstructions to the existence of non-trivial infinitesimal deformations and prove rigidity results for certain homogeneous $G_2$-instantons. |
| title | Homogeneous G2 and Sasakian instantons on the Stiefel 7-manifold |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2406.06753 |