Roland Hildebrand

collaborators

3 papers

math.CA2026

Sufficient conditions for the existence of exponential-polynomial expansions for solutions of certain differential equations

Roland Hildebrand, Rahaf Habib

We consider ordinary differential equations (ODE) of the form $u^{''} u - (u^{'})^{2} = e^{- x} P (u) - 1$ , where $P$ is a polynomial. In previous work, necessary conditions on $P$ have been e…

math.CA2026

Necessary conditions for the existence of exponential-polynomial expansions for solutions of certain differential equations

Rahaf Habib, Roland Hildebrand

We consider ordinary differential equations (ODE) of the form $u^{''} u - (u^{'})^{2} = e^{- x} P (u) - 1$ , where $P$ is a polynomial. For $P = u^{k}$ , $k = 3, 4, 6$ this ODE is equivalent to cert…

math.DG2024

Half-dimensional immersions into the para-complex projective space and Ruh-Vilms type theorems

Josef F. Dorfmeister, Roland Hildebrand, Shimpei Kobayashi

In this paper we study isometric immersions $f : M^{n} \to C^{'} P^{n}$ of an $n$ -dimensional pseudo-Riemannian manifold $M^{n}$ into the $n$ -dimensional para-complex pro…