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arXiv · 1607.05644

Locally 2-fold symmetric manifolds are locally symmetric

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.

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Shaoqiang Deng, Vladimir S. Matveev. 2016-07-19. Locally 2-fold symmetric manifolds are locally symmetric. https://doi.org/10.1007/s00013-017-1036-1

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