Projective Vector Field

(Differential Geometry)

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Differential Geometry
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What is Projective vector field?

A projective vector field (projective) is a smooth vector field on a semi Riemannian manifold (p.ex. spacetime) whose flow preserves the geodesic structure of without necessarily preserving the affine parameter of any geodesic. More intuitively, the flow of the projective maps geodesics smoothly into geodesics without preserving the affine parameter.

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differential geometry

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