Abstract
We study the spectral geometry of smooth maps of a compact Riemannian manifold in a Euclidean space, by using the notion of order (introduced by the first author). We give some best possible estimates of energy and total tension of a map in terms of order. Some applications to closed curves and harmonic maps are then obtained. In the last section, we relate the spectral geometry of the Gauss map of a submanifold to its topology and derive some topological obstructions to submanifolds to have a Gauss map of low type.
