Some transformations on manifolds with almost contact and contact metric structures, II

For the notations we conform to the previous paper By we denote the group of all diffeomorphisms which leave of the structure tensors (,,) invariant in an almost contact manifold M. We assume always that the dimension of the manifold is greater or equal to 3. In 4, we shall see that is a Lie transformation group if M is a contact Riemannian manifold, and some structures of this group are considered. In 6, for an arbitrary point x of a contact Riemannian manifold M and an element of , we shall search for the relation between the scalar curvature R x at x and R x at x by lengthy calculations. As applications, in 7, we treat some contact Riemannian manifolds which are supposed to satisfy certain conditions, for examples, being of constant scalar curvature, or being an Einstein space, etc.. Then, with some exceptions, it is shown that coincides with the group of all automorphisms.