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Least Squares Approximation of Flatness on Riemannian Manifolds

Author

Listed:
  • Iulia Hirica

    (Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest 1, Romania
    These authors contributed equally to this work.)

  • Constantin Udriste

    (Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, RO-060042 Bucharest 6, Romania
    These authors contributed equally to this work.
    Second address: Academy of Romanian Scientists, Ilfov 3, RO-050044 Bucharest 5, Romania.)

  • Gabriel Pripoae

    (Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest 1, Romania
    These authors contributed equally to this work.)

  • Ionel Tevy

    (Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, RO-060042 Bucharest 6, Romania
    These authors contributed equally to this work.)

Abstract

The purpose of this paper is fourfold: (i) to introduce and study the Euler–Lagrange prolongations of flatness PDEs solutions (best approximation of flatness) via associated least squares Lagrangian densities and integral functionals on Riemannian manifolds; (ii) to analyze some decomposable multivariate dynamics represented by Euler–Lagrange PDEs of least squares Lagrangians generated by flatness PDEs and Riemannian metrics; (iii) to give examples of explicit flat extremals and non-flat approximations; (iv) to find some relations between geometric least squares Lagrangian densities.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1757-:d:426906
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    References listed on IDEAS

    as
    1. Constantin Udriste & Ionel Tevy, 2020. "Geometric Dynamics on Riemannian Manifolds," Mathematics, MDPI, vol. 8(1), pages 1-14, January.
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    Cited by:

    1. Sergei Aliukov & Anatoliy Alabugin & Konstantin Osintsev, 2022. "Review of Methods, Applications and Publications on the Approximation of Piecewise Linear and Generalized Functions," Mathematics, MDPI, vol. 10(16), pages 1-43, August.

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    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.

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