Affine submanifolds and the Theorem of Cartan-Ambrose-Hicks
Pawel, Knut ; Reckziegel, Helmut
Kodai Math. J., Tome 25 (2002) no. 2, p. 341-356 / Harvested from Project Euclid
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In this article E.\,Cartan's theorem about the existence of (local) totally geodesic sub\-mani\-folds with a prescribed tangent plane is generalized to manifolds which are equipped only with a linear connection; there is also given a global version of the theorem. The results are used for a short and geometric proof of the Theorem of Cartan-Ambrose-Hicks, and more generally of a generalization which is concerned with the existence of affine maps of arbitrary rank.
Publié le : 2002-10-14
Classification:  
@article{1071674466,
     author = {Pawel, Knut and Reckziegel, Helmut},
     title = {Affine submanifolds and the Theorem of Cartan-Ambrose-Hicks},
     journal = {Kodai Math. J.},
     volume = {25},
     number = {2},
     year = {2002},
     pages = { 341-356},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1071674466}
}

Pawel, Knut; Reckziegel, Helmut. Affine submanifolds and the Theorem of Cartan-Ambrose-Hicks. Kodai Math. J., Tome 25 (2002) no. 2, pp.  341-356. http://gdmltest.u-ga.fr/item/1071674466/