On symmetries of the Heisenberg group
classification
🧮 math.DG
keywords
classifyfieldsgroupheisenbergvectoraffinecasualcharacter
read the original abstract
We consider the three-dimensional Heisenberg group, equipped with any left-invariant metric, either Lorentzian or Riemannian. We completely classify their affine vector fields and investigate their relationship with Killing vector fields and their casual character. We also classify their Ricci, curvature and matter collineations, proving that there are no nontrivial examples.
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