Timeline for How does the concept of a hermitian metric generalize to a hyperkahler manifold?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| May 12, 2020 at 20:30 | comment | added | Malkoun | I just saw your question now, $3$ years later! You would like to have relations similar to the quaternions, such as $IJ=K$ or, if you prefer, $I_1 I_2 = I_3$ and cyclic permutations, together with the relations $I_1^2 = -I_1$ and so on. By the way, suppose you have $I_1$, $I_2$ and $I_3$ satisfying the usual relations, and would like to construct new almost complex structures, say $I'_1$, $I'_2$ and $I'_3$ satisfying $I'_1 I'_2 = -I'_3$ and cyclic, just take $I'_1 = I_1$, $I'_2 = I_2$ and $I'_3 = -I_3$ for example. So this sign is thus not so important. I do like to get signs right though. | |
| Aug 3, 2017 at 13:10 | history | edited | Malkoun | CC BY-SA 3.0 |
I have also done the calculation using an alternate notation convention.
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| Aug 3, 2017 at 11:38 | comment | added | Mtheorist | It seems that some references use the convention where each complex structure is represented as ${(J_u)_i}^s$ instead of ${(J_u)^s}_i$. It seems that when we use this convention, the second term in the answer you gave has a plus sign in front of it instead of a minus sign. Is this correct? | |
| Aug 2, 2017 at 11:57 | vote | accept | Mtheorist | ||
| Aug 2, 2017 at 11:50 | history | edited | Malkoun | CC BY-SA 3.0 |
I have added a direct answer to the OP's main question.
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| Aug 2, 2017 at 10:42 | history | edited | Malkoun | CC BY-SA 3.0 |
added 243 characters in body
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| Aug 2, 2017 at 10:35 | history | answered | Malkoun | CC BY-SA 3.0 |