Recurrent tensors and holonomy group

D.K. Datta
1974 Bulletin of the Australian Mathematical Society  
Let M be a connected C manifold of dimension n with a linear connection V . A method is being introduced here to study the action of the holonomy group and the restricted holonomy group of V on a recurrent tensor. The main result of this paper is that if the recurrence covector M of a recurrent tensor S on M is an exact form then the tensor S is invariant under the holonomy group of F and if H is a closed form then 5 is invariant under the restricted holonomy group of F . In the last section,
more » ... is result is applied to some particular cases including the case of a riemannian manifold with recurrent curvature.
doi:10.1017/s0004972700040648 fatcat:kz6qilhcjncilcbduyj7jdwa2u