The distribution of eigenvalues of partial differential operators
In this paper, we prove that the first eigenvalue of a complete spacelike submanifold in with the bounded Gauss map must be zero.
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.