Timeline for Possible sign of scalar curvature for Einstein warped product manifold with Ricci-flat
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 21, 2022 at 2:20 | history | became hot network question | |||
| Feb 20, 2022 at 21:15 | comment | added | MathDG | An obvious result that might interest you, even if it doesn't answer your question, is the following: An Einstein warped-product manifold where the base is a Riemannian manifold, independently of dimension, and the fiber is Ricci-flat, we have: $|\nabla f|^2+[\frac{\lambda (m-n)+ R}{m(m-1)}]f^2=0$ (with $n$ and $m$ the dimension of the base and the fiber, respectively and $R$ is the scalar curvature of the base). Then, either $R$ $\leq$ $\lambda (n − m)$ or $f$ is trivial. | |
| Feb 20, 2022 at 21:04 | vote | accept | MathDG | ||
| Feb 20, 2022 at 19:42 | answer | added | Vitali Kapovitch | timeline score: 3 | |
| Feb 20, 2022 at 18:20 | history | asked | MathDG | CC BY-SA 4.0 |