6 research outputs found
SOME NEW IDENTITIES FOR THE SECOND COVARIANT DERIVATIVE OF THE CURVATURE TENSOR
In this paper we study the second covariant derivative of Riemannian curvature tensor. Some new identities for the second covariant derivative are given. Namely, identities obtained by cyclic sum with respect to three indices are given. In the first 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
Novel invariants for almost geodesic mappings of the third type
Two kinds of invariance for geometrical objects under transformations are
involved in this paper. With respect to these kinds, we obtained novel
invariants for almost geodesic mappings of the third type of a non-symmetric
affine connection space in this paper. Our results are presented in two
sections. In the Section 3, we obtained the invariants for the equitorsion
almost geodesic mappings which do not have the property of reciprocity. In the
Section 4, we obtained the invariants for almost geodesic mappings of the third
type which have the property of reciprocity.Comment: 18 pages, 0 figure