Timeline for Tangent bundle with Sasaki metric is Kähler iff $M$ is locally flat
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| May 17, 2020 at 3:20 | vote | accept | MOULI Kawther | ||
| S May 16, 2020 at 23:20 | history | suggested | Gabe K | CC BY-SA 4.0 |
Fixed a typo
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| May 16, 2020 at 23:09 | review | Suggested edits | |||
| S May 16, 2020 at 23:20 | |||||
| May 16, 2020 at 23:08 | answer | added | Gabe K | timeline score: 4 | |
| May 16, 2020 at 23:02 | comment | added | MOULI Kawther | assuming the connection used is the Levi-Civita connection connection, can you please help me with the proof? | |
| May 16, 2020 at 22:37 | comment | added | Gabe K | Right. Choosing a connection is equivalent to choosing the connection coefficients $\Gamma_{jk}^i$. The point is that the theorem is only true when the connection used is the Levi-Civita connection. | |
| May 16, 2020 at 22:13 | comment | added | MOULI Kawther | actully $D$ represents covariant differentiation: $Dv^{i}=dv^{i}+Γ_{jk}^{i}v^{j}dx^{k}$ | |
| May 16, 2020 at 22:06 | comment | added | Gabe K | By $D$, you mean the Levi-Civita connection, right? Otherwise, for an arbitrary affine connection, the requirement for the Sasaki metric to be Kahler is for $D$ to be flat and to be Codazzi-coupled to the metric $g$. | |
| May 16, 2020 at 21:44 | history | edited | YCor | CC BY-SA 4.0 |
formatting
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| May 16, 2020 at 21:33 | history | asked | MOULI Kawther | CC BY-SA 4.0 |