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Lorenzo Pellegrino

Publications and source records attributed to Lorenzo Pellegrino.

5 recordsLinked to original sources
arXiv2025

Ricci solitons of special Lorentzian Lie groups with a four-dimensional isometry group

In the framework of the study of homogeneous Lorentzian three-manifolds, we consider here the only class of examples which admit a four-dimensional group of isometries but are neither Lorentzian Bianchi-Cartan-Vranceanu spaces nor plane waves. We obtain an explicit description in global coordinates of these special homogeneous Lorentzian manifolds. We then prove that all such examples are non-gradient expanding Ricci solitons.

math.DG↗
arXiv2025

Helix surfaces in Lorentzian Heisenberg group

In this work we investigate constant angle surfaces in the Lorentzian Heisenberg group $\htt$. After providing a complete description of the geometry of the ambient space, we perform the full classification of minimal and CMC helix surfaces in $\htt$, giving their explicit parametrizations. In addition, we investigate the constant angle spacelike and timelike surfaces for a Lorentzian metric on the Heisenberg group $H_3$ not treated before in the literature, first showing that such surfaces have constant Gaussian curvature and then obtaining their complete characterization.

math.DG↗
arXiv2023

Helix surfaces for Berger-like metrics on the anti-de Sitter space

We consider the Anti-de Sitter space $\mathbb{H}^3_1$ equipped with Berger-like metrics, that deform the standard metric of $\mathbb{H}^3_1$ in the direction of the hyperbolic Hopf vector field. Helix surfaces are the ones forming a constant angle with such vector field. After proving that these surfaces have (any) constant Gaussian curvature, we achieve their explicit local description in terms of a one-parameter family of isometries of the space and some suitable curves. These curves turn out to be general helices, which meet at a constant angle the fibers of the hyperbolic Hopf fibration.

math.DG↗