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KILLING MAGNETIC TRAJECTORIES IN 3D EGOROV SPACES

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Abstract

The paper is devoted to explore the trajectories of charged particles varying under the influence of Lorentz force of Killing magnetic fields (i.e., closed 2-form corresponding to Killing vector fields) in Egorov 3-spaces. Predominantly, we characterize Killing vector fields and hence determine magnetic trajectories in some Killing magnetic fields on Egorov 3-spaces. We also obtain magnetic trajectories in some Killing magnetic backgrounds on flat Egorov 3-spaces.

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Notes

  1. A Lorentzian manifold \((\mathbb {R}^n,g^f)\), where \(f:\mathbb {R} \rightarrow (0,\infty )\) is smooth and \(g^f \equiv f(x^n) \sum _{i=1}^{n-2} (dx^i)^2 + 2 dx^{n-1} dx^n\), is called an Egorov space named after Ivan Petrovich Egorov who introduced such manifolds in [13].

  2. In the remaining portion of this article, KVF stands for Killing vector field.

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Acknowledgements

I would like to express my sincere thanks to Prof. Subenoy Chakraborty (Jadavpur University) and Dr. Joydeep Sengupta (Aliah University) for enlightening me with their pearls of wisdom and helping me in various directions.

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  1. Department of Mathematics, Kaliyaganj College, Kaliyaganj, Uttar Dinajpur, 733129, West Bengal, India

    Zafar Iqbal

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Iqbal, Z. KILLING MAGNETIC TRAJECTORIES IN 3D EGOROV SPACES. J Math Sci 271, 322–340 (2023). https://doi.org/10.1007/s10958-023-06468-0

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