Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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

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

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.

Leave a public comment
Send a private comment to the author(s)
* All users must log in before leaving a comment
Views 0
Downloads 0
Comments 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.