Some new identities for the second covariant derivative of the curvature tensor

Abstract

In this paper, we have studied the second covariant derivative of Riemannian curvature tensor. Some new identities for the second covariant derivative have been given. Namely, identities obtained by cyclic sum with respect to three indices have been given. In the rst case, two curvature tensor indices and one covariant derivative index participate in the cyclic sum, while in the second case one curvature tensor index and two covariant derivative indices participate in the cyclic sum.