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.
@article{bwmeta1.element.bwnjournal-article-apmv67z2p111bwm,
author = {Jerzy Kalina and Antoni Pierzchalski and Pawe\l\ Walczak},
title = {Only one of generalized gradients can be elliptic},
journal = {Annales Polonici Mathematici},
volume = {66},
year = {1997},
pages = {111-120},
zbl = {0901.53017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv67z2p111bwm}
}
Jerzy Kalina; Antoni Pierzchalski; Paweł Walczak. Only one of generalized gradients can be elliptic. Annales Polonici Mathematici, Tome 66 (1997) pp. 111-120. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv67z2p111bwm/
[000] [P] B. Ørsted and A. Pierzchalski, The Ahlfors Laplacian on a Riemannian manifold, in: Constantin Carathéodory: An International Tribute, World Sci., Singapore, 1991, 1020-1048. | Zbl 0746.53012
[001] [P] A. Pierzchalski, Ricci curvature and quasiconformal deformations of a Riemannian manifold, Manuscripta Math. 66 (1989), 113-127. | Zbl 0698.53021
[002] [SW] E. M. Stein and G. Weiss, Generalization of the Cauchy-Riemann equations and representation of the notation group, Amer. J. Math. 90 (1968), 163-197.
[003] [We] H. Weyl, The Classical Groups, Princeton Univ. Press, Princeton, 1946.