ArticleOriginal scientific text
Title
Only one of generalized gradients can be elliptic
Authors 1, 1, 2
Affiliations
- Institute of Mathematics, Technical University of Łódź, Al. Politechniki 11, 93-590 Łódź, Poland
- Institute of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland
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.
Keywords
connection, group representation, Young diagram, elliptic operator
Bibliography
- [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.
- [P] A. Pierzchalski, Ricci curvature and quasiconformal deformations of a Riemannian manifold, Manuscripta Math. 66 (1989), 113-127.
- [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.
- [We] H. Weyl, The Classical Groups, Princeton Univ. Press, Princeton, 1946.
Pages:
111-120
Main language of publication
English
Received
1995-02-10
Published
1997
Exact and natural sciences