Helical geodesic immersions of semi-Riemannian manifolds

Miura, Kouhei

Miura, Kouhei

Kodai Math. J., Tome 30 (2007) no. 1, p. 322-343 / Harvested from Project Euclid

Résumé

We obtain some basic results on helical geodesic immersions in semi-Riemannian geometry. For example, it is shown that, for an indefinite semi-Riemannian submanifold, if any space-like geodesics of the submanifold are helices of order d, curvatures λ₁,...,λ_d-1 and signatures ε₁,...,ε_d in the ambient space, then any time-like geodesics of the submanifold have the same order and curvatures, and signatures (-1)¹ε₁,...,(-1)^dε_d.

Publié le : 2007-10-14
Classification:

@article{1193924937,
     author = {Miura, Kouhei},
     title = {Helical geodesic immersions of semi-Riemannian manifolds},
     journal = {Kodai Math. J.},
     volume = {30},
     number = {1},
     year = {2007},
     pages = { 322-343},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1193924937}
}

Miura, Kouhei. Helical geodesic immersions of semi-Riemannian manifolds. Kodai Math. J., Tome 30 (2007) no. 1, pp.  322-343. http://gdmltest.u-ga.fr/item/1193924937/