Lesson plan
Geodesic map
In mathematics—specifically, in differential geometry—a geodesic map (or geodesic mapping or geodesic diffeomorphism) is a function that "preserves geodesics". More precisely, given two (pseudo-)Riemannian manifolds (M, g) and (N, h), a function φ : M → N is said to be a geodesic map if * φ is a diffeomorphism of M onto N; and * the image under φ of any geodesic arc in M is a geodesic arc in N; and * the image under the inverse function φ −1 of any geodesic arc in N is a geodesic arc in M.
Article summary
In mathematics—specifically, in differential geometry—a geodesic map (or geodesic mapping or geodesic diffeomorphism) is a function that "preserves geodesics". More precisely, given two (pseudo-)Riemannian manifolds (M, g) and (N, h), a function φ : M → N is said to be a geodesic map if * φ is a diffeomorphism of M onto N; and * the image under φ of any geodesic arc in M is a geodesic arc in N; and * the image under the inverse function φ −1 of any geodesic arc in N is a geodesic arc in M.
Key claims
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.