Curvature-homogeneous pseudo-Riemannian manifold
From Diffgeom
Template:Pseudo-Riemannian metric property
Definition
A pseudo-Riemannian manifold is said to be curvature-homogeneous up to order if for any points there exists a linear isometry such that for all integers the following holds:
where denotes the covariant derivative with respect to the Levi-Civita connection and denotes the Riemann curvature tensor.
A pseudo-Riemannian manifold is simply termed curvature-homogeneous if it is curvature-homogeneous up to order zero.
References
- Infinitesimally homogeneous spaces by I M Singerm Commun. Pure Appl. Math. 13 685 - 97 (1960)