Harmonic Hadamard manifolds and Gauss hypergeometric differential equations

TL;DR

This paper introduces a new class of harmonic Hadamard manifolds characterized by hypergeometric equations, providing a Fourier transform inversion formula and a volume density characterization.

Contribution

It defines harmonic Hadamard manifolds of hypergeometric type and establishes their Fourier analysis framework and geometric properties.

Findings

Harmonic Hadamard manifolds of hypergeometric type are characterized by Gauss hypergeometric equations.

An inversion formula for the spherical Fourier transform on these manifolds is derived.

A volume density characterization of hypergeometric type manifolds is provided.

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.