Answer by whpowell96 for Is a map that preserves torsion and curvature of all...
Note that this condition implies that all circles of radius $r$ must map to circles of radius $r$ under $F$. We show that if the map is not an isometry, then we can find a circle that maps to a...
View ArticleIs a map that preserves torsion and curvature of all smooth curves an isometry?
In my introductory differential geometry class, we learnt that isometries preserve the torsion $\tau$ and curvature $\kappa$ of curves. I was wondering if the converse of this statement is true: if a...
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