## Tsukuba Journal of Mathematics

### Generalized helical immersions of a Riemannian manifold all of whose geodesics are closed into a Euclidean space

Naoyuki Koike

#### Abstract

In this paper, we investigate an isometric immersion of a compact connected Riemannian manifold $M$ into a Euclidean space and a sphere such that every geodesic in $M$ is closed and viewed as a helix (of general order) in the ambient space.

#### Article information

Source
Tsukuba J. Math., Volume 22, Number 3 (1998), 811-824.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496163682

Digital Object Identifier
doi:10.21099/tkbjm/1496163682

Mathematical Reviews number (MathSciNet)
MR1674059

Zentralblatt MATH identifier
0935.53024

#### Citation

Koike, Naoyuki. Generalized helical immersions of a Riemannian manifold all of whose geodesics are closed into a Euclidean space. Tsukuba J. Math. 22 (1998), no. 3, 811--824. doi:10.21099/tkbjm/1496163682. https://projecteuclid.org/euclid.tkbjm/1496163682