Differential geometry MOC
Isometry of a semi-Riemannian manifold
Let be a semi-Riemannian -manifold.
An isometry is a -diffeomorphism which preserves the metric, #m/def/geo/diff
i.e. the pullback satisfyies .
The isometries form a Lie group ,
whose corresponding Lie algebra consists of Killing fields.
Proof
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