$S^1$-invariant Laplacian flow
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866912091433074688 |
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| author | Fowdar, Udhav |
| author_facet | Fowdar, Udhav |
| contents | The Laplacian flow is a geometric flow introduced by Bryant as a way for finding torsion free $G_2$-structures. If the flow is $S^1$-invariant then it descends to a flow of $SU(3)$-structures on a $6$-manifold. In this article we derive expressions for these evolution equations. In our search for examples we discover the first inhomogeneous shrinking solitons, which are also gradient. We also show that any compact non-torsion free soliton admits no infinitesimal symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_05130 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | $S^1$-invariant Laplacian flow Fowdar, Udhav Differential Geometry 53C10, 53C29 The Laplacian flow is a geometric flow introduced by Bryant as a way for finding torsion free $G_2$-structures. If the flow is $S^1$-invariant then it descends to a flow of $SU(3)$-structures on a $6$-manifold. In this article we derive expressions for these evolution equations. In our search for examples we discover the first inhomogeneous shrinking solitons, which are also gradient. We also show that any compact non-torsion free soliton admits no infinitesimal symmetry. |
| title | $S^1$-invariant Laplacian flow |
| topic | Differential Geometry 53C10, 53C29 |
| url | https://arxiv.org/abs/2007.05130 |