Flatness produced by some geometric PDEs
Abstract
This paper has several goals. The first idea is to study the geometric PDEs of connection-flatness, curvature-flatness, Ricci-flatness, scalar curvature-flatness in a modern and rigorous way. Although the idea is not new, our main Theorems about flatness introduce a different point of view in Differential Geometry. The second idea is to introduce and study the Euler-Lagrange prolongations of PDEs-flatness solutions via associated least squares Lagrangian densities and functionals on Riemannian manifolds. All geometric PDEs turned into one of the most intensively developing branches of modern differential geometry.
Cite
@article{arxiv.1911.03254,
title = {Flatness produced by some geometric PDEs},
author = {Iulia Hirica and Constantin Udriste and Gabriel Pripoae and Ionel Tevy},
journal= {arXiv preprint arXiv:1911.03254},
year = {2019}
}
Comments
24 pages; Key words: geometric PDEs, connection-flatness, curvature-flatness, Ricci-flatness, scalar curvature-flatness, least squares Lagrangian density, adapted metrics and connections