pseudo-Riemannian manifold

A pseudo-Riemannian manifold is a smooth manifold equipped with a nondegenerate, symmetric metric tensor of arbitrary signature that allows measurement of lengths and angles, including those with indefinite sign as in spacetime geometry.

Aliases (3)

• Lorentzian metric ×2
• Riemannian manifold ×1
• type D Petrov spacetime ×1

Instances (5)

• Kerr metric ("Lorentzian metric")
• Reissner–Nordström metric ("Lorentzian metric")
• Kähler manifold ("Riemannian manifold")
• Kerr–Newman black hole ("type D Petrov spacetime")
• Minkowski space-time