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The Globalization Problem of the Hamilton–DeDonder–Weyl Equations on a Local k-Symplectic Framework

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Abstract

In this paper, we aim at addressing the globalization problem of Hamilton–DeDonder–Weyl equations on a local k-symplectic framework and we introduce the notion of locally conformal k-symplectic (l.c.k-s.) manifolds. This formalism describes the dynamical properties of physical systems that locally behave like multi-Hamiltonian systems. Here, we describe the local Hamiltonian properties of such systems, but we also provide a global outlook by introducing the global Lee one-form approach. In particular, the dynamics will be depicted with the aid of the Hamilton–Jacobi equation, which is specifically proposed in a l.c.k-s manifold.

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Acknowledgements

We gratefully acknowledge anonymous referees for their valuable comments which definitely make this paper more correct and easy to read. This work has been partially supported by MINECO Grants MTM2016-76-072-P and the ICMAT Severo Ochoa Project SEV-2011-0087 and SEV-2015-0554.

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Authors and Affiliations

  1. Department of Mathematics, Gebze Technical University, 41400, Gebze, Kocaeli, Turkey

    Oğul Esen

  2. Consejo Superior de Investigaciones Científicas and Real Academia Española de las Ciencias, Instituto de Ciencias Matemáticas, Campus Cantoblanco, C/Nicolás Cabrera, 13-15, 28049, Madrid, Spain

    Manuel de León

  3. Consejo Superior de Investigaciones Científicas, Instituto de Ciencias Matemáticas, Campus Cantoblanco, C/Nicolás Cabrera 13-15, 28049, Madrid, Spain

    Cristina Sardón

  4. Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093, Warsaw, Poland

    Marcin Zając

Authors
  1. Oğul Esen
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  2. Manuel de León
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  3. Cristina Sardón
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  4. Marcin Zając
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Correspondence to Oğul Esen.

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Esen, O., de León, M., Sardón, C. et al. The Globalization Problem of the Hamilton–DeDonder–Weyl Equations on a Local k-Symplectic Framework. Mediterr. J. Math. 18, 26 (2021). https://doi.org/10.1007/s00009-020-01685-2

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  • DOI: https://doi.org/10.1007/s00009-020-01685-2

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