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How is this fact derived?

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- Thread starter center o bass
- Start date

- #1

- 560

- 2

How is this fact derived?

- #2

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One first finds an equation for the second derivative of Killing vector ξ. This means that ξ anywhere is a function of ξ and its first derivative at some point. The defining equation for ξ constrains the first derivative of ξ to be antisymmetric or sort-of antisymmetric where ξ itself is 0. For n space dimensions:

- Possible values of ξ: n
- Possible values of the antisymmetrized first derivative of ξ: n(n-1)/2

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