Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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)

How to cite: Hirica, I.; Udrişte, C.; Pripoae, G.; Tevy, I. Least Squares Approximation of Flatness on Riemannian Manifolds. Preprints 2020, 2020090234 (doi: 10.20944/preprints202009.0234.v1). Hirica, I.; Udrişte, C.; Pripoae, G.; Tevy, I. Least Squares Approximation of Flatness on Riemannian Manifolds. Preprints 2020, 2020090234 (doi: 10.20944/preprints202009.0234.v1).

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.

Subject Areas

geometric flatness; least squares Lagrangian densities; adapted metrics and connections

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