Английская Википедия:Curvature collineation
Материал из Онлайн справочника
Шаблон:Short description A curvature collineation (often abbreviated to CC) is vector field which preserves the Riemann tensor in the sense that,
- <math>\mathcal{L}_X R^a{}_{bcd}=0</math>
where <math>R^a{}_{bcd}</math> are the components of the Riemann tensor. The set of all smooth curvature collineations forms a Lie algebra under the Lie bracket operation (if the smoothness condition is dropped, the set of all curvature collineations need not form a Lie algebra). The Lie algebra is denoted by <math>CC(M)</math> and may be infinite-dimensional. Every affine vector field is a curvature collineation.
See also
- Conformal vector field
- Homothetic vector field
- Killing vector field
- Matter collineation
- Spacetime symmetries
Шаблон:Relativity-stub
Шаблон:Math-physics-stub
