Timeline for Does any warped product metric with harmonic Weyl curvature admit a structure of zero radial Weyl curvature?
Current License: CC BY-SA 4.0
5 events
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| Dec 6, 2023 at 17:27 | comment | added | Matheus Andrade | I thought about that but I haven't had the time yet to do these computations, I'm temporarily obligated to other stuff at the moment. But I do suspect if $B$ is one-dimensional, then $W(\bullet, \bullet, \bullet, \nabla h) = 0$. | |
| Dec 6, 2023 at 16:17 | comment | added | Willie Wong | Have you computed the case where $B$ is one dimensional? Harmonic Weyl is equivalent to the Cotton tensor vanishing. The Ricci curvature of a warped product with one dimensional $B$ and Einstein $N$ can be computed very explicitly. So can the Riemann and Weyl curvatures. Whether what you are looking for holds should be fairly obvious. | |
| Dec 6, 2023 at 15:37 | history | edited | Matheus Andrade | CC BY-SA 4.0 |
added 55 characters in body
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| Dec 4, 2023 at 18:15 | history | edited | Matheus Andrade | CC BY-SA 4.0 |
edited title
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| Dec 2, 2023 at 3:52 | history | asked | Matheus Andrade | CC BY-SA 4.0 |