Lemma 3.17 . [0509] Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
Source coverage notes Source fidelity gap: the original arXiv HTML omits an author TeX footnote attached to equation e:def-omega, including its reference to Remark r:error-function. The retained HTML is preserved as published; the original author TeX remains available. TeX correspondence is not complete. Complete original source context · Original author HTML
Lemma 3.17 .
(3.154) Ω i j α β ( 1 2 r d y β α ^ − 1 2 r 3 y μ y β d y μ α ^ ) \displaystyle\Omega_{ij\alpha\beta}(\frac{1}{2r}dy_{\widehat{\beta\alpha}}-\frac{1}{2r^{3}}y_{\mu}y_{\beta}dy_{\widehat{\mu\alpha}}) = − Ω i j α β ( 1 4 r d y α β ^ + 1 4 r 2 y α β ^ d r ) , \displaystyle=-\Omega_{ij\alpha\beta}(\frac{1}{4r}dy_{\widehat{\alpha\beta}}+\frac{1}{4r^{2}}y_{\widehat{\alpha\beta}}dr),
(3.155) 1 2 r 3 A i j α β y β y μ d y μ α ^ \displaystyle\frac{1}{2r^{3}}A_{ij\alpha\beta}y_{\beta}y_{\mu}dy_{\widehat{\mu\alpha}} = A i j α β ( 1 4 r 2 y α β ^ d r − 1 4 r d y α β ^ ) . \displaystyle=A_{ij\alpha\beta}(\frac{1}{4r^{2}}y_{\widehat{\alpha\beta}}dr-\frac{1}{4r}dy_{\widehat{\alpha\beta}}).