Abel ordinary differential equation, differential algebra and projective connections

Abel ordinary differential equation, differential algebra and projective connections

We firstly study the Abel ordinary differential equations of the first and second kind from the perspectives of differential algebra. Then using differential geometry we exhibit some relations between the Abel ordinary differential equation of the first kind and projective connections on surfaces wh...

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Veröffentlicht in:Bulletin des sciences mathématiques 2025-03, Vol.199, p.103567, Article 103567
1. Verfasser: Wone, Oumar
Format: Artikel
Sprache:eng
Schlagworte:
Abel equation
Algebraic solutions
First integrals
Projective connections
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Zusammenfassung:We firstly study the Abel ordinary differential equations of the first and second kind from the perspectives of differential algebra. Then using differential geometry we exhibit some relations between the Abel ordinary differential equation of the first kind and projective connections on surfaces which allow us to find a “Darboux first integral” of the Abel differential equation.
ISSN:0007-4497
DOI:10.1016/j.bulsci.2024.103567