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math.DG2017★ 1 cited
On symmetries of the Heisenberg group
Wafaa Batat, Amirhesam Zaeim
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…
math.DG2017★ 1 cited
Totally umbilical surfaces in three-manifolds with a parallel null vector field
Wafaa Batat, Stuart James Hall
We study non-degenerate, totally umbilical surfaces of a special class of pseudo-Riemannian manifolds, namely Walker three-manifolds. We show that such surfaces are either one of a…