Geodesics on metrics of Eguchi–Hanson type

Abstract

Geodesic equations are solved when at least two of theta , phi and psi are constant, or r is constant, on scalar flat metrics of Eguchi–Hanson type. They can also be solved also on Eguchi–Hanson metrics which are Ricci flat if only phi is constant. However, the explicit solution of the geodesic equations is not available yet if only psi is constant.