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Least Squares Approximation of Flatness on Riemannian Manifolds

A peer-reviewed version of this preprint was published in:
Mathematics 2020, 8(10), 1757. https://doi.org/10.3390/math8101757

Submitted:

09 September 2020

Posted:

10 September 2020

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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
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