Differential geometry MOC

Differential pullback along a diffeomorphism

Let be a -diffeomorphism. For a mixed tensor field , the pullback is defined by #m/def/geo/diff

The pushforward can be defined via the inverse so that

Further terminology

• If and , we say is a symmetry transformation of the tensor field .
• In the particular case for the metric tensor, we say is an isometry of .

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