arXiv subjects

Genki Ishikawa

Publications and source records attributed to Genki Ishikawa.

2 recordsLinked to original sources

arXiv2025

Stability analysis for the pseudo-Riemannian geodesic flows of step-two nilpotent Lie groups

The present paper deals with the stability analysis for the geodesic flow of a step-two nilpotent Lie group equipped with a left-invariant pseudo-Riemannian metric. The Lie-Poisson equation can be described in terms of the so-called $j$-mapping, a linear operator associated to the step-two nilpotent Lie algebras equipped with the induced scalar product. The stability of equilibrium points for the Hamilton equation is determined in terms of their Williamson types.

math.DS↗

arXiv2024

An elliptic fibration arising from the Lagrange top and its monodromy

This paper is to investigate an elliptic fibration over $\mathbb{CP}^2$ arising from the Lagrange top from the viewpoint of complex algebraic geometry. The description of the discriminant locus of this elliptic fibration is given in detail. Moreover, the concrete description of the discriminant locus and the complete classification of singular fibres of the elliptic fibration are obtained according to Miranda's theory of elliptic threefolds after suitable modifications of the base and total spaces. Furthermore, the monodromy of the elliptic fibration is described.

math-ph↗