Kodai Mathematical Journal

Helical geodesic immersions of semi-Riemannian manifolds

Kouhei Miura

Full-text: Open access

Abstract

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,...,λd-1 and signatures ε1,...,εd in the ambient space, then any time-like geodesics of the submanifold have the same order and curvatures, and signatures (-1)1ε1,...,(-1)dεd.

Article information

Source
Kodai Math. J., Volume 30, Number 3 (2007), 322-343.

Dates
First available in Project Euclid: 1 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1193924937

Digital Object Identifier
doi:10.2996/kmj/1193924937

Mathematical Reviews number (MathSciNet)
MR2372121

Zentralblatt MATH identifier
1138.53045

Citation

Miura, Kouhei. Helical geodesic immersions of semi-Riemannian manifolds. Kodai Math. J. 30 (2007), no. 3, 322--343. doi:10.2996/kmj/1193924937. https://projecteuclid.org/euclid.kmj/1193924937


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