Only one of generalized gradients can be elliptic

• Autorzy: Jerzy Kalina , Antoni Pierzchalski , Paweł Walczak
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

connection; group representation; Young diagram; elliptic operator

Kategorie tematyczne

• 53C05: Connections, general theory
• 20G05: Representation theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1997
• Tom: 67
• Numer: 2
• Strony: 111-120

Daty

wydano

1997

otrzymano

1995-02-10

Twórcy

autor

Jerzy Kalina

• Institute of Mathematics, Technical University of Łódź, Al. Politechniki 11, 93-590 Łódź, Poland

autor

Antoni Pierzchalski

• Institute of Mathematics, Technical University of Łódź, Al. Politechniki 11, 93-590 Łódź, Poland

autor

Paweł Walczak

• Institute of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland

Bibliografia

• [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.