Geodesic
Submanifold theory and parallel transport
Kragujevac Journal of Mathematics, Tome 37 (2013) no. 1, p. 33

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

A geometrical interpretation of semi-parallel submanifolds is presented in terms of parallel transport of the second fundamental form around an infinitesimal coordinate parallelogram. Further, a new scalar curvature invariant of the immersion is introduced. Isotropy of this invariant at every point means that the submanifold is pseudo-parallel.
Classification : 53A55 53B20 53C42
Keywords: Submanifolds, semi-parallel, pseudo-parallel, parallel transport. 
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     title = {Submanifold theory and parallel transport},
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Franki Dillen; Johan Fastenakels; Stefan Haesen; Joeri Van der Veken; Leopold Verstraelen. Submanifold theory and parallel transport. Kragujevac Journal of Mathematics, Tome 37 (2013) no. 1, p. 33 . http://geodesic.mathdoc.fr/item/KJM_2013_37_1_a2/