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February, 2019 Dynamics of Riemannian $1$-foliations on $3$-manifolds
Jaeyoo Choy, Hahng-Yun Chu
Taiwanese J. Math. 23(1): 145-157 (February, 2019). DOI: 10.11650/tjm/180605

Abstract

In this paper we study several dynamical properties of a Riemannian $1$-dimensional foliation $\mathcal{L}$ on an oriented closed $3$-manifold $M$. Carrière [6] classified such pairs $(M,\mathcal{L})$. Using the classification we describe in detail recurrence points, $\omega$-limit sets and attractors. Finally, using the fact that the Poincaré map on a transversal surface for a Riemannian $1$-dimensional foliation is an isometry, we show the nonhyperbolicity of $(M,\mathcal{L})$.

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Jaeyoo Choy. Hahng-Yun Chu. "Dynamics of Riemannian $1$-foliations on $3$-manifolds." Taiwanese J. Math. 23 (1) 145 - 157, February, 2019. https://doi.org/10.11650/tjm/180605

Information

Received: 17 September 2017; Accepted: 11 June 2018; Published: February, 2019
First available in Project Euclid: 12 July 2018

zbMATH: 1405.37052
MathSciNet: MR3909994
Digital Object Identifier: 10.11650/tjm/180605

Subjects:
Primary: 37D05
Secondary: 37F75, 53C12

Rights: Copyright © 2019 The Mathematical Society of the Republic of China

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Vol.23 • No. 1 • February, 2019
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