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December 2008 Isometric Immersions with Geodesic Normal Sections in Semi-Riemannian Geometry
Kouhei MIURA
Tokyo J. Math. 31(2): 479-488 (December 2008). DOI: 10.3836/tjm/1233844064

Abstract

We study an isometric immersion $f:M \to \bar{M}$ with geodesic normal sections, where $\bar{M}$ is a semi-Riemannian space form. In Riemannian geometry, it is known that $f$ is helical, in particular, all geodesics of $M$ have the same proper order in $\bar{M}$. However this does not hold in general, when $\bar{M}$ is indefinite semi-Riemannian. We give sufficient conditions for an isometric immersion with geodesic normal sections to be helical.

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Kouhei MIURA. "Isometric Immersions with Geodesic Normal Sections in Semi-Riemannian Geometry." Tokyo J. Math. 31 (2) 479 - 488, December 2008. https://doi.org/10.3836/tjm/1233844064

Information

Published: December 2008
First available in Project Euclid: 5 February 2009

zbMATH: 1171.53038
MathSciNet: MR2477884
Digital Object Identifier: 10.3836/tjm/1233844064

Subjects:
Primary: 53C50
Secondary: 53C40

Rights: Copyright © 2008 Publication Committee for the Tokyo Journal of Mathematics

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Vol.31 • No. 2 • December 2008
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