Green's function for the Hodge Laplacian on some classes of Riemannian and Lorentzian symmetric spaces

Details Green's function for the Hodge Laplacian on some classes of Riemannian and Lorentzian symmetric spaces Green's function for the Hodge Laplacian on some classes of Riemannian and Lorentzian symmetric spaces

2008-07-14

arxiv.org/abs/0807.2187v1

Comm. Math. Phys. 290 (2009) 105-127

Mathematics

Analysis of PDEs

18 pages

Scientific paper

We compute the Green's function for the Hodge Laplacian on the symmetric spaces M\times\Sigma, where M is a simply connected n-dimensional Riemannian or Lorentzian manifold of constant curvature and \Sigma is a simply connected Riemannian surface of constant curvature. Our approach is based on a generalization to the case of differential forms of the method of spherical means and on the use of Riesz distributions on manifolds. The radial part of the Green's function is governed by a fourth order analogue of the Heun equation.

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