Harmonic Hadamard Manifolds and Gauss Hypergeometric Differential Equations

Abstract

A new class of harmonic Hadamard manifolds, those spaces called hypergeometric type, is defined in terms of Gauss hypergeometric equations. A spherical Fourier transform defined on harmonic Hadamard manifolds of hypergeometric type admits an inversion formula. A characterization of the harmonic Hadamard manifold as of hypergeometric type is obtained with respect to volume density.