The eta invariant and the equivariant unitary bordism of spherical space form groups
Several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the symmetries of geometric structures and differential equations. A general result clarifying this effect in the case when the structure is associated to a vector distribution, is proposed.
We introduce an explicit procedure to generate natural operators on manifolds with almost Hermitian symmetric structures and work out several examples of this procedure in the case of almost Grassmannian structures.