Magnetic curves on tangent sphere bundles

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas volume 113, pages2087–2112(2019)Cite this article

Abstract

In this paper we investigate contact magnetic curves on the unit tangent bundle UM of a Riemannian manifold M and we write the magnetic equations. In the case when M is a space form M(c), it follows that every contact normal magnetic curve is slant when \(c=1\), while for \(c\ne 1\) a contact normal magnetic curve is slant if and only if it satisfies a conservation law. We perform a detailed study of contact magnetic curves in \(U{{\mathbb {S}}}^2\).

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Acknowledgements

The second author is supported by the project funded by the Ministry of Research and Innovation within Program 1–Development of the national RD system, Subprogram 1.2–Institutional Performance–RDI excellence funding projects, Contract no. 34PFE/19.10.2018.

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Affiliations

  1. Institute of Mathematics, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8571, Japan

    Jun-ichi Inoguchi

  2. Faculty of Mathematics, University ‘Al. I. Cuza’ of Iasi, Bd. Carol I, No. 11, 700506, Iasi, Romania

    Marian Ioan Munteanu

Authors
  1. Jun-ichi Inoguchi
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  2. Marian Ioan Munteanu
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Corresponding author

Correspondence to Marian Ioan Munteanu.

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Dedicated to professor Vladimir Rovenski on the occasion of his 65th anniversary.

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Inoguchi, Ji., Munteanu, M.I. Magnetic curves on tangent sphere bundles. RACSAM 113, 2087–2112 (2019). https://doi.org/10.1007/s13398-018-0600-2

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Keywords

  • Magnetic field
  • Tangent sphere bundle
  • \(\alpha \)-Sasakian manifold
  • Periodic curve

Mathematics Subject Classification

  • 53B21
  • 53C15
  • 53C25
  • 53C80