•  
  •  
 

Turkish Journal of Mathematics

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.

DOI

10.55730/1300-0098.3285

Keywords

Einstein, curvature identity, curvature tenso

First Page

2530

Last Page

2544

Included in

Mathematics Commons

Share

COinS