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Harmonic vector fields on compact Lorentz surfaces

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Abstract

We study harmonic vector fields on a Lorentzian torus T 2 i.e. critical points of the total bending functional \({\mathcal {B} : \mathcal {E} \to \mathbb {R}}\) were \({\mathcal {E}}\) consists of all unit timelike vector fields on T 2. We derive the first variation formula for \({\mathcal {B}}\) in terms of the Lorentz angle function associated to each \({X \in \mathcal {E}}\) and give applications on flat Lorentzian tori.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi della Basilicata, Viale dell’Ateneo Lucano 10, Campus Macchia Romana, 85100, Potenza, Italy

    Sorin Dragomir

  2. Faculté des Sciences Techniques, Université François Rabelais, Parc de Grandmont, 37200, Tours, France

    Marc Soret

Authors
  1. Sorin Dragomir
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  2. Marc Soret
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Correspondence to Sorin Dragomir.

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Dragomir, S., Soret, M. Harmonic vector fields on compact Lorentz surfaces. Ricerche mat. 61, 31–45 (2012). https://doi.org/10.1007/s11587-011-0113-1

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  • DOI: https://doi.org/10.1007/s11587-011-0113-1

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