Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3285
Abstract
Patterson discussed the curvature identities on Riemannian manifolds based on the skew-symmetric properties of the generalized Kronecker delta, and a curvature identity for any 6-dimensional Riemannian manifold was independently derived from the Chern-Gauss-Bonnet Theorem. In this paper, we provide the explicit formulae of Patterson's curvature identity that holds on 5-dimensional and 6-dimensional Einstein manifolds. We confirm that the curvature identities on the Einstein manifold derived from the Chern-Gauss-Bonnet Theorem are the same as the curvature identities deduced from Patterson's result. We also provide examples that support the theorems.
Keywords
Einstein, curvature identity, curvature tenso
First Page
2530
Last Page
2544
Recommended Citation
EUH, YUNHEE; KIM, JIHUN; and PARK, JEONGHYEONG
(2022)
"Curvature identities for Einstein manifolds of dimensions 5 and 6,"
Turkish Journal of Mathematics: Vol. 46:
No.
6, Article 33.
https://doi.org/10.55730/1300-0098.3285
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss6/33
