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Least Squares Approximation of Flatness on Riemannian Manifolds
Version 1
: Received: 9 September 2020 / Approved: 10 September 2020 / Online: 10 September 2020 (10:41:58 CEST)
A peer-reviewed article of this Preprint also exists.
Hirica, I.; Udriste, C.; Pripoae, G.; Tevy, I. Least Squares Approximation of Flatness on Riemannian Manifolds. Mathematics 2020, 8, 1757. Hirica, I.; Udriste, C.; Pripoae, G.; Tevy, I. Least Squares Approximation of Flatness on Riemannian Manifolds. Mathematics 2020, 8, 1757.
Abstract
The purpose of this paper is threefold: (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.
Keywords
geometric flatness; least squares Lagrangian densities; adapted metrics and connections
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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