Geometric flows of G2-structures on 3-Sasakian 7-manifolds
<p>A 3-Sasakian structure on a 7-manifold may be used to define two distinct Einstein metrics: the 3-Sasakian metric and the squashed Einstein metric. Both metrics are induced by nearly parallel G<sub>2</sub>-structures which may also be expressed in terms of the 3-Sasakian structu...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Elsevier
2023
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| Summary: | <p>A 3-Sasakian structure on a 7-manifold may be used to define two distinct Einstein metrics: the 3-Sasakian metric and the squashed Einstein metric. Both metrics are induced by nearly parallel G<sub>2</sub>-structures which may also be expressed in terms of the 3-Sasakian structure. Just as Einstein metrics are critical points for the Ricci flow up to rescaling, nearly parallel G<sub>2</sub>-structures provide natural critical points of the (rescaled) geometric flows of G<sub>2</sub>-structures known as the Laplacian flow and Laplacian coflow. We study each of these flows in the 3-Sasakian setting and see that their behaviour is markedly different, particularly regarding the stability of the nearly parallel G<sub>2</sub>-structures. We also compare the behaviour of the flows of G<sub>2</sub>-structures with the (rescaled) Ricci flow.</p> |
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