Horospherical mean curvature functions and D'Atri spaces

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Bibliographic Details
Main Authors:	Knieper, Gerhard, Park, JeongHyeong, Peyerimhoff, Norbert
Format:	Preprint
Published:	2025
Subjects:	Differential Geometry 53C24
Online Access:	Acceder al recurso
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author	Knieper, Gerhard Park, JeongHyeong Peyerimhoff, Norbert
author_facet	Knieper, Gerhard Park, JeongHyeong Peyerimhoff, Norbert
contents	We consider simply connected Riemannian manifolds without conjugate points for which the horospherical mean curvature function is continuous, reversible and invariant under the geodesic flow. We show under mild additional curvature tensor conditions that rank one manifolds in this family are automatically asymptotically harmonic. In particular, compact rank one manifolds of this kind must be locally symmetric spaces of negative curvature. Moreover, we show under the same conditions that rank one D'Atri spaces without conjugate points are harmonic. An earlier result of this type was proved by Druetta for certain homogeneous D'Atri spaces.
format	Preprint
id	arxiv_https___arxiv_org_abs_2510_04572
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Horospherical mean curvature functions and D'Atri spaces Knieper, Gerhard Park, JeongHyeong Peyerimhoff, Norbert Differential Geometry 53C24 We consider simply connected Riemannian manifolds without conjugate points for which the horospherical mean curvature function is continuous, reversible and invariant under the geodesic flow. We show under mild additional curvature tensor conditions that rank one manifolds in this family are automatically asymptotically harmonic. In particular, compact rank one manifolds of this kind must be locally symmetric spaces of negative curvature. Moreover, we show under the same conditions that rank one D'Atri spaces without conjugate points are harmonic. An earlier result of this type was proved by Druetta for certain homogeneous D'Atri spaces.
title	Horospherical mean curvature functions and D'Atri spaces
topic	Differential Geometry 53C24
url	https://arxiv.org/abs/2510.04572

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