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Geodesic manifold

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at a point

A submanifold of a smooth manifold (Riemannian or with an affine connection) such that the geodesic lines (cf. Geodesic line) of that are tangent to at have a contact of at least the second order with . This requirement is fulfilled at all points if any geodesic in is also a geodesic in . Such geodesic manifolds are called totally geodesic manifolds.


Comments

Also called geodesic submanifold and totally geodesic submanifold, respectively.

References

[a1] W. Klingenberg, "Riemannian geometry" , Springer (1982) (Translated from German)
How to Cite This Entry:
Geodesic manifold. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Geodesic_manifold&oldid=31980
This article was adapted from an original article by Yu.A. Volkov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article