11 papers
Cross-ratios and first order ordinary differential equations
Oumar Wone
We investigate the usefulness of the cross-ratio in the study of first order odes of the form $y^\prime=P_ny^n+P_{n-1}y^{n-1}+\ldots+P_1y+P_0,\;\; (P_i)_{0\leqslant i\leqslant n}\i…
Holomorphic projective connections on surfaces and osculating spaces
Oumar Wone
We study complex analytic projective connections on surfaces in projective n-spaces in terms of the "second" neighborhood of the surface in the ambient space, and in terms of the o…
Lectures on Finslerian Geometry
Oumar Wone
Lecture notes on Finsler Geometry
The Birkhoff-Grothendieck theorem
Oumar Wone
We give a historical presentation of the Grothendieck theorem on the splitting of vector bundles over the Riemann sphere, and explore some of its links with the Riemann-Hilbert-Bir…
Some remarkable autonomous systems
Oumar Wone
We study the links of the Darboux-Halphen-Ramanujan system, with contact geometry, canonical coordinates of some -dimensional Frobenius manifolds and projective connections on R…
Representation Theory and Differential Equations
Ahmed Sebbar, Oumar Wone
We study the geometry and partial differential equations arising from the consideration of group-determinants, and representation theory. The simplest and most striking such exampl…
Geometric Methods in Partial Differential Equations
Ahmed Sebbar, Daniele Struppa, Oumar Wone
We study the interplay between geometry and partial differential equations. We show how the fundamental ideas we use require the ability to correctly calculate the dimensions of sp…
Frobenius determinants and Bessel Functions
Ahmed Sebbar, Oumar Wone
We study the geometry and partial differential equations arising from the consideration of Frobenius determinants, also called-group-determinants. This leads us to address some asp…
Holomorphic projective connections on surfaces
Oumar Wone
We study complex analytic (possibly singular) projective connections on the plane. We characterize some of them in terms of their families of integral curves. We also give a beginn…
Anharmonic Solutions to the Riccati equation and elliptic modular functions
Ahmed Sebbar, Oumar Wone
We study algebraic solutions of the Riccati equation over the field of rational functions , and over the elliptic function field .
Affine geometry of second order ODEs
Oumar Wone
We apply the Cartan equivalence method to the study of real analytic second order ODEs under the local real analytic diffeomorphism of $\C^2$ which are area-preserving. This enable…