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An application of Lovelock’s theorem. (English) Zbl 1099.53014
Summary: We employ a theorem of D. Lovelock [J. Math. Phys. 13, 874–876 (1972; Zbl 0234.53020)] to obtain the Lanczos identity [C. Lanczos, Ann. Math. (2) 39, 842–850 (1938; Zbl 0019.37904, JFM 64.0767.03)] $${^*R^*}_{ijpq} R^{ajpq}= \frac14 \delta_t^a$$ which is valid in every Riemannian 4-space.
##### MSC:
 53B20 Local Riemannian geometry 53B15 Other connections
##### Keywords:
Einstein tensor; Lanczos identity