Timeline for Complex manifolds whose tangent and cotangent bundles are isomorphic as complex vector bundles
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 23, 2022 at 23:39 | history | became hot network question | |||
| Nov 23, 2022 at 21:43 | answer | added | Misha Verbitsky | timeline score: 7 | |
| Nov 23, 2022 at 21:12 | comment | added | Ben McKay | Robert's example is often called a Hopf manifold. | |
| Nov 23, 2022 at 15:55 | comment | added | Robert Bryant | Well, it doesn't have to be Kähler. For example, if you consider the compact manifold that you get by removing the origin from $\mathbb{C}^n$ ($n>1$) and dividing by the $\mathbb{Z}$-action of $n\cdot z = 2^n\,z$, that manifold, diffeomorphic to $S^1\times S^{2n-1}$, has $TX\simeq T^*X$ as complex bundles, but it is not holomorphic symplectic (or even Kähler). | |
| Nov 23, 2022 at 15:37 | history | asked | Jost Schultze | CC BY-SA 4.0 |