JournalsprimsVol. 55, No. 3pp. 531–564

Harmonic Hadamard Manifolds and Gauss Hypergeometric Differential Equations

  • Mitsuhiro Itoh

    University of Tsukuba, Ibaraki, Japan

  • Hiroyasu Satoh

    Nippon Institute of Technology, Saitama, Japan
Harmonic Hadamard Manifolds and Gauss Hypergeometric Differential Equations cover

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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.

Cite this article

Mitsuhiro Itoh, Hiroyasu Satoh, Harmonic Hadamard Manifolds and Gauss Hypergeometric Differential Equations. Publ. Res. Inst. Math. Sci. 55 (2019), no. 3, pp. 531–564

DOI 10.4171/PRIMS/55-3-3