Locally 2-fold symmetric manifolds are locally symmetric

Shaoqiang Deng; Vladimir S. Matveev

doi:10.1007/s00013-017-1036-1

Locally 2-fold symmetric manifolds are locally symmetric

Differential Geometry 2018-02-05 v1

Authors: Shaoqiang Deng , Vladimir S. Matveev

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Abstract

A manifold is locally \emph{ $k$ -fold symmetric}, if for any point and any $k$ -dimensional vector subspace tangent to this point there exists a local isometry such that this point is a fixed point and the differential of the isometry restricted to that $k$ -dimensional vector subspace is minus the identity. We show that for $k \ge 2$ , Riemannian, pseudoriemannian and Finslerian locally $k$ -fold symmetric manifolds are locally symmetric.

Keywords

locally k-fold symmetric locally symmetric local isometry Riemannian manifold pseudoriemannian manifold Finslerian manifold

Cite

@article{arxiv.1607.05644,
  title  = {Locally 2-fold symmetric manifolds are locally symmetric},
  author = {Shaoqiang Deng and Vladimir S. Matveev},
  journal= {arXiv preprint arXiv:1607.05644},
  year   = {2018}
}

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