Comment on GL(2,R) geometry of 4th order ODEs
Pawel Nurowski
TL;DR
This paper explores a special class of fourth-order ordinary differential equations characterized by contact invariants, linking them to Ricci tensors of gl(2,R)-valued connections, and provides explicit nonhomogeneous examples.
Contribution
It introduces a novel geometric characterization of certain 4th order ODEs using Ricci tensors of gl(2,R) connections, extending Bryant's contact invariant conditions.
Findings
Characterization of 4th order ODEs via Ricci tensor of gl(2,R) connections
Explicit nonhomogeneous examples of such ODEs
Connection between contact invariants and geometric structures
Abstract
We describe 4th order ODEs satisfying two contact invariant conditions of Bryant in terms of the Ricci tensor of a certain gl(2,R) valued connection. We also provide nonhomogeneous examples of such ODEs.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Advanced Topics in Algebra · Ophthalmology and Eye Disorders