Английская Википедия:Curvature collineation

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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


Шаблон:Relativity-stub Шаблон:Math-physics-stub