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Bibliographic Details
Main Authors:	Xu, Ming, Deng, Shaoqiang
Format:	Preprint
Published:	2025
Subjects:	Differential Geometry
Online Access:	https://arxiv.org/abs/2506.09471
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_version_	1866908404152270848
author	Xu, Ming Deng, Shaoqiang
author_facet	Xu, Ming Deng, Shaoqiang
contents	We construct a counter example to show that the Homogeneity Conjecture, first proposed by J.A. Wolf in 1962, is not true. To be precise, we prove that on the Lie group Sp(2), there exists a left invariant Riemannian metric and a cyclic subgroup Γ of order (2n+1), such that the left translation of each element of Γ on Sp(2) is a Clifford-Wolf translation, but the Riemannian quotient Γ\Sp(2) is not homogeneous.
format	Preprint
id	arxiv_https___arxiv_org_abs_2506_09471
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	A counter example for the Homogeneity Conjecture Xu, Ming Deng, Shaoqiang Differential Geometry We construct a counter example to show that the Homogeneity Conjecture, first proposed by J.A. Wolf in 1962, is not true. To be precise, we prove that on the Lie group Sp(2), there exists a left invariant Riemannian metric and a cyclic subgroup Γ of order (2n+1), such that the left translation of each element of Γ on Sp(2) is a Clifford-Wolf translation, but the Riemannian quotient Γ\Sp(2) is not homogeneous.
title	A counter example for the Homogeneity Conjecture
topic	Differential Geometry
url	https://arxiv.org/abs/2506.09471

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