On conformally symmetric 2-Ricci-recurrent spaces
We study invariant contact -spheres on principal circle-bundles and solve the corresponding existence problem in dimension 3. Moreover, we show that contact - spheres can only exist on -dimensional manifolds and we construct examples of contact -spheres on such manifolds. We also consider relations between tautness and roundness, a regularity property concerning the Reeb vector fields of the contact forms in a contact -sphere.
The author studies relations between the following two types of natural operators: 1. Natural operators transforming vector fields on manifolds into vector fields on a natural bundle ; 2. Natural operators transforming vector fields on manifolds into functions on the cotangent bundle of . It is deduced that under certain assumptions on , all natural operators of the second type can be constructed through those of the first one.