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10 papers
On the Jacobi Elliptic functions and Applications
A. Raouf Chouikha
In this paper we are interested in developments of elliptic functions of Jacobi. In particular a trigonometric expansion of the classical theta functions introduced by the author (…
Ricci Curvature and Singularities of Constant Scalar Curvature Metrics
A. Raouf Chouikha
In this work we consider periodic spherically symmetric metrics of constant positive scalar curvature on the n-dimensional cylinder called pseudo-cylindric metrics. These metrics b…
Remark on a conjecture of conformal transformations of Riemannian manifolds
A. Raouf Chouikha
Ejiri gave a negative answer to a conjecture of Lichnerowicz concerning Riemannian manifolds with constant scalar curvature admitting an infinitesimal non isometric conformal trans…
Isochronous Centers of Lienard Type Equations and Applications
A. Raouf Chouikha
In this work we study the equation with a center at 0 and investigate conditions of its isochronicity. When and are analytic (not n…
Expansions of Theta Functions and Applications
A. Raouf Chouikha
We prove that the classical theta function may be expressed as $$ θ_4(v,τ) = θ_4(0,τ) \exp[- \sum_{p\geq 1} \sum_{k\geq 0} \frac {1}{p} \bigg(\frac {\sin πv}{(\sin (k+{1/2})π…
On the Existence of Certain Metrics with Non Parallel Ricci Tensor
A. Raouf Chouikha
A. Derdzinki [D] gave examples of Riemannian metrics with harmonic curvature and non parallel Ricci tensor on some compact manifolds . We examine their existence as well as…