Preserve one, preserve all

2019/09/11 by Mainkar, Meera, Schmidt, Benjamin
#51K10 #53C22 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1909.05276

Abstract

Isometries of metric spaces (X,d) preserve all level sets of d. We formulate and prove cases of a conjecture asserting if X is a complete Riemannian manifold, then a function f:X → X preserving at least one level set d^-1(r), with r>0 small enough, is an isometry.

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