Riccati PDEs That Imply Curvature-Flatness

Iulia Hirica, Constantin Udriste, Gabriel Pripoae and Ionel Tevy
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Iulia Hirica: Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, Sector 1, RO-010014 Bucharest, Romania
Constantin Udriste: Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, Sector 6, RO-060042 Bucharest, Romania
Gabriel Pripoae: Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, Sector 1, RO-010014 Bucharest, Romania
Ionel Tevy: Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, Sector 6, RO-060042 Bucharest, Romania

Mathematics, 2021, vol. 9, issue 5, 1-19

Abstract: In this paper the following three goals are addressed. The first goal is to study some strong partial differential equations (PDEs) that imply curvature-flatness, in the cases of both symmetric and non-symmetric connection. Although the curvature-flatness idea is classic for symmetric connection, our main theorems about flatness solutions are completely new, leaving for a while the point of view of differential geometry and entering that of PDEs. The second goal is to introduce and study some strong partial differential relations associated to curvature-flatness. The third goal is to introduce and analyze some vector spaces of exotic objects that change the meaning of a generalized Kronecker delta projection operator, in order to discover new PDEs implying curvature-flatness. Significant examples clarify some ideas.

Keywords: curvature-flatness PDEs; Riccati PDEs; generalized Kronecker delta; eigentensors; metrics and connections adapted to flatness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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