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Geodesic-preserving homothety that is not a local isometry

A nonunit Euclidean dilation sends straight-line geodesics to straight-line geodesics but scales their tangent inner products. Preservation of geodesics alone therefore does not imply local isometry.

Ancestors (8)

  1. Geodesic preservation by a local isometry
  2. Local isometry
  3. First fundamental form
  4. Differential geometry
  5. Geometry and topology
  6. Area of mathematics
  7. Mathematics
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