HARMONIC HADAMARD MANIFOLDS OF PRESCRIBED RICCI CURVATURE AND VOLUME ENTROPY

Mitsuhiro ITOH; Sinhwi KIM; Jeonghyeong PARK; Hiroyasu SATOH

doi:10.2206/kyushujm.70.267

Kyushu Journal of Mathematics

Online ISSN : 1883-2032
Print ISSN : 1340-6116
ISSN-L : 1340-6116

HARMONIC HADAMARD MANIFOLDS OF PRESCRIBED RICCI CURVATURE AND VOLUME ENTROPY

Mitsuhiro ITOH, Sinhwi KIM, Jeonghyeong PARK, Hiroyasu SATOH

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Keywords: Hadamard manifold, volume entropy, harmonic manifold, hyperbolic space, asymptotically harmonic manifold, hypergeometric type

JOURNAL FREE ACCESS

2016 Volume 70 Issue 2 Pages 267-280

DOI https://doi.org/10.2206/kyushujm.70.267

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Abstract

A harmonic, Kähler Hadamard manifold (M²^m, g), m ≥ 2, with Ricci curvature Ric =−(m + 1)/2 and volume entropy ρ(M, g)= m, is biholomorphically isometric to a complex hyperbolic space of holomorphic sectional curvature −1, provided (M, g) is of hypergeometric type. A similar characterization of the real hyperbolic space and the quaternionic hyperbolic space is also obtained in terms of Ricci curvature and volume entropy, without hypergeometric assumption.

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