Harmonic Hadamard manifolds and Gauss hypergeometric differential equations
arXiv:1808.00625
Abstract
A new class of harmonic Hadamard manifolds, those spaces called of hypergeometric type, is defined in terms of Gauss hypergeometric equations. Spherical Fourier transform defined on a harmonic Hadamard manifold of hypergeometric type admits an inversion formula. A characterization of harmonic Hadamard manifold being of hypergeometric type is obtained with respect to volume density.
33 pages. To appear in Publications of the Research Institute for Mathematical Sciences (Publ.RIMS)