A new proof of the classification of Elliptic Foliations induced by real Quadratic Fields with center

TL;DR

This paper presents a new unified proof for classifying elliptic foliations induced by real quadratic fields, expanding understanding of foliation structures with a novel approach and identifying a linear family with unique properties.

Contribution

It introduces a unified technique for classifying elliptic foliations and constructs a linear family with a non-invariant tangency set, extending prior classifications.

Findings

Unified proof technique for elliptic foliations

Classification of foliations induced by real quadratic fields

Identification of a linear family with a non-invariant tangency set

Abstract

In this work, we give a new proof of the classification of the Lotka-Volterra and Reversible foliations, originally given by Gautier. This new proof, involves an unified technique for both cases, using the theory of foliations. In addition, we obtain a linear family of elliptical foliations with a non-invariant tangency set.