Only one of generalized gradients can be elliptic
Volume 67 / 1997
Annales Polonici Mathematici 67 (1997), 111-120
DOI: 10.4064/ap-67-2-111-120
Abstract
Decomposing the space of k-tensors on a manifold M into the components invariant and irreducible under the action of GL(n) (or O(n) when M carries a Riemannian structure) one can define generalized gradients as differential operators obtained from a linear connection ∇ on M by restriction and projection to such components. We study the ellipticity of gradients defined in this way.
