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Geometric Dynamics on Riemannian Manifolds

Author

Listed:
  • Constantin Udriste

    (Department of Mathematics-Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, 060042 Bucharest, Romania)

  • Ionel Tevy

    (Department of Mathematics-Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, 060042 Bucharest, Romania)

Abstract

The purpose of this paper is threefold: (i) to highlight the second order ordinary differential equations (ODEs) as generated by flows and Riemannian metrics (decomposable single-time dynamics); (ii) to analyze the second order partial differential equations (PDEs) as generated by multi-time flows and pairs of Riemannian metrics (decomposable multi-time dynamics); (iii) to emphasise second order PDEs as generated by m -distributions and pairs of Riemannian metrics (decomposable multi-time dynamics). We detail five significant decomposed dynamics: (i) the motion of the four outer planets relative to the sun fixed by a Hamiltonian, (ii) the motion in a closed Newmann economical system fixed by a Hamiltonian, (iii) electromagnetic geometric dynamics, (iv) Bessel motion generated by a flow together with an Euclidean metric (created motion), (v) sinh-Gordon bi-time motion generated by a bi-flow and two Euclidean metrics (created motion). Our analysis is based on some least squares Lagrangians and shows that there are dynamics that can be split into flows and motions transversal to the flows.

Suggested Citation

  • Constantin Udriste & Ionel Tevy, 2020. "Geometric Dynamics on Riemannian Manifolds," Mathematics, MDPI, vol. 8(1), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:79-:d:304811
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    References listed on IDEAS

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    1. Constantin Udrişte & Ana-Maria Teleman, 2004. "Hamiltonian approaches of field theory," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-12, January.
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    Cited by:

    1. Iulia Hirica & Constantin Udriste & Gabriel Pripoae & Ionel Tevy, 2021. "Riccati PDEs That Imply Curvature-Flatness," Mathematics, MDPI, vol. 9(5), pages 1-19, March.
    2. Iulia Hirica & Constantin Udriste & Gabriel Pripoae & Ionel Tevy, 2020. "Least Squares Approximation of Flatness on Riemannian Manifolds," Mathematics, MDPI, vol. 8(10), pages 1-18, October.

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