An application of topological paley-wiener theorems to invariant differential equations on symmetric spaces

1979 ◽  
pp. 192-206 ◽  
Author(s):  
Masaaki Eguchi
Keyword(s):  
Differential Equations ◽  
Symmetric Spaces ◽  
Invariant Differential

A Tensor Equation of Elliptic Type

1953 ◽  
Vol 5 ◽  
pp. 524-535 ◽  
Author(s):  
G. F. D. Duff
Keyword(s):  
Riemannian Manifold ◽  
Differential Equations ◽  
Tensor Field ◽  
Differential Operators ◽  
Elliptic Type ◽  
Tensor Equation ◽  
Tensor Theory ◽  
Elliptic Differential Equations ◽  
Invariant Differential ◽  
Image Position

The theory of the systems of partial differential equations which arise in connection with the invariant differential operators on a Riemannian manifold may be developed by methods based on those of potential theory. It is therefore natural to consider in the same context the theory of elliptic differential equations, in particular those which are self-adjoint. Some results for a tensor equation in which appears, in addition to the operator Δ of tensor theory, a matrix or double tensor field defined on the manifold, are here presented. The equation may be writtenin a notation explained below.

Harmonic Spinors on Hyperbolic Space

1993 ◽  
Vol 36 (3) ◽  
pp. 257-262 ◽  
Author(s):  
Pierre-Yves Gaillard
Keyword(s):  
Differential Equations ◽  
Symmetric Space ◽  
Representation Theory ◽  
Hyperbolic Space ◽  
Harmonic Functions ◽  
Short Note ◽  
Harmonic Forms ◽  
Semisimple Symmetric Space ◽  
Invariant Differential ◽  
Harmonic Spinors

AbstractThe purpose for this short note is to describe the space of harmonic spinors on hyperbolicn-spaceHn. This is a natural continuation of the study of harmonic functions onHnin [Minemura] and [Helgason]—these results were generalized in the form of Helgason's conjecture, proved in [KKMOOT],—and of [Gaillard 1, 2], where harmonic forms onHnwere considered. The connection between invariant differential equations on a Riemannian semisimple symmetric spaceG/Kand homological aspects of the representation theory ofG, as exemplified in (8) below, does not seem to have been previously mentioned. This note is divided into three main parts respectively dedicated to the statement of the results, some reminders, and the proofs. I thank the referee for having suggested various improvements.

scholarly journals Conformal and Geodesic Mappings onto Some Special Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 664 ◽  
Author(s):  
Volodymyr Berezovski ◽  
Yevhen Cherevko ◽  
Lenka Rýparová
Keyword(s):  
Differential Equations ◽  
Closed System ◽  
Symmetric Spaces ◽  
Conformal Mappings ◽  
Cauchy Type ◽  
Affine Connections ◽  
Covariant Derivatives ◽  
Riemannian Spaces

In this paper, we consider conformal mappings of Riemannian spaces onto Ricci-2-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-2-symmetric spaces. The main equations for the mappings are obtained as a closed system of Cauchy-type differential equations in covariant derivatives. We find the number of essential parameters which the solution of the system depends on. A similar approach was applied for the case of conformal mappings of Riemannian spaces onto Ricci-m-symmetric Riemannian spaces, as well as geodesic mappings of spaces with affine connections onto Ricci-m-symmetric spaces.

Sign in / Sign up

Export Citation Format

Share Document