https://neckpinch.com/authors/amir-babak-aazami/New arXiv papers by Amir Babak Aazami, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2007.00071/arxiv:2007.00071Tue, 30 Jun 2020 00:00:00 GMTAmir Babak Aazami — On a smooth n-manifold M with n ≥ 3, we study pairs (g,T) consisting of a Riemannian metric g and a unit length closed vector field T. Motivated by how Ricci solitons generalize Einstein metrics via a distinguished vector field, we propose to generalize space forms by considering those pairs (g,T) whose corresponding Lorentzian metric g_(scriptscriptstyle L) = g − 2T^(flat) ⊗ T^(flat) has constant curvature. We show by examples that such pairs exist when M is noncompact, and that complete metrics exist among them. When M is compact, however, the situation is more rigid. In the compact setting, we prove that the only pairs (g,T) whose corresponding Lorentzian metric g_(scriptscriptstyle L) is a space form are those where (M,g) is flat and its universal covering splits isometrically as a product ℝ × N. The nonexistence of compact Lorentzian spherical space forms plays a key role in our proof.Ricci solitonsEinstein metricsSphere theoremsBoundaries & non-compactPhysics